qu.1.topic=Sequences and Series@

qu.1.1.mode=Inline@
qu.1.1.name=Finite Series (Closed Form)@
qu.1.1.comment=<p>Recall the following closed form formulas</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>N</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>N</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><mi>k</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>N</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>k</mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>M</mi></mrow><mrow><mi>N</mi></mrow></munderover><mfenced open='(' close=')' separators=','><mrow><msub><mi>a</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msub><mi>a</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msub><mi>a</mi><mrow><mi>N</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msub><mi>a</mi><mrow><mi>M</mi></mrow></msub></mrow></mstyle></math></p>@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$a=[30,40,50,60,70];
$picka=switch(rint(5),$a);
$b=$picka+1;
$ANS1=$picka*$b/2;
$c=[20,30,40,50,60,70,80];
$pickc=switch(rint(7),$c);
condition: ne($picka,$pickc);
$ANS2=$picka*$pickc;
$d=rint(2,6);
$e=[5,6,7,8,9];
$picke=switch(rint(5),$e);
$f=$picke+1;
$ANS3="$d^($f)-$d";@
qu.1.1.uid=b9d7b43d-f0a8-42b1-bd46-8a99bece33ab@
qu.1.1.weighting=1,1,1@
qu.1.1.numbering=alpha@
qu.1.1.part.1.name=sro_id_1@
qu.1.1.part.1.maple_answer=$ANS1@
qu.1.1.part.1.editing=useHTML@
qu.1.1.part.1.question=(Unset)@
qu.1.1.part.1.libname=@
qu.1.1.part.1.mode=Maple@
qu.1.1.part.1.allow2d=1@
qu.1.1.part.1.plot=@
qu.1.1.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.1.part.1.type=formula@
qu.1.1.part.2.name=sro_id_2@
qu.1.1.part.2.maple_answer=$ANS2@
qu.1.1.part.2.editing=useHTML@
qu.1.1.part.2.question=(Unset)@
qu.1.1.part.2.libname=@
qu.1.1.part.2.mode=Maple@
qu.1.1.part.2.allow2d=1@
qu.1.1.part.2.plot=@
qu.1.1.part.2.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.1.part.2.type=formula@
qu.1.1.part.3.name=sro_id_3@
qu.1.1.part.3.maple_answer=$ANS3@
qu.1.1.part.3.editing=useHTML@
qu.1.1.part.3.question=(Unset)@
qu.1.1.part.3.libname=@
qu.1.1.part.3.mode=Maple@
qu.1.1.part.3.allow2d=1@
qu.1.1.part.3.plot=@
qu.1.1.part.3.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.1.part.3.type=formula@
qu.1.1.question=<p>Use the closed form formulas to evaluate the following series:</p><p>(i) <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>$picka</mi></mrow></munderover><mi>n</mi></mrow></mstyle></math> = <span>&nbsp;</span><1><span>&nbsp;</span></p><p><span>(ii) <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>$picka</mi></mrow></munderover><mi>$pickc</mi></mrow></mstyle></math></span> = <span>&nbsp;</span><2><span>&nbsp;</span></p><p><span>(iii) <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>$picke</mi></mrow></munderover><mfenced open='(' close=')' separators=','><mrow><msup><mi>$d</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>$d</mi><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math></span> = <span>&nbsp;</span><3><span>&nbsp;</span></p><p><span>For (iii) you do not have to simplify the exponents in the answer. (i.e., You could enter 5^8 instead of 390625).</span></p>@

qu.1.2.mode=Inline@
qu.1.2.name=Finite Series (Closed Form) iii@
qu.1.2.comment=<p>Recall the following closed form formulas</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>N</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>N</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><mi>k</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>N</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>k</mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>M</mi></mrow><mrow><mi>N</mi></mrow></munderover><mfenced open='(' close=')' separators=','><mrow><msub><mi>a</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msub><mi>a</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msub><mi>a</mi><mrow><mi>N</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msub><mi>a</mi><mrow><mi>M</mi></mrow></msub></mrow></mstyle></math></p>@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$a=[30,40,50,60,70];
$picka=switch(rint(5),$a);
$b=$picka+1;
$ANS1=$picka*$b/2;
$c=[20,30,40,50,60,70,80];
$pickc=switch(rint(7),$c);
condition: ne($picka,$pickc);
$ANS2=$picka*$pickc;
$d=rint(2,6);
$e=[6,7,8,9,10];
$picke=switch(rint(5),$e);
$f=$picke+1;
$ANS3="$d^($f)-$d";@
qu.1.2.uid=b9359a23-33f1-4093-8a49-dc6e387dfe19@
qu.1.2.weighting=1,1,1@
qu.1.2.numbering=alpha@
qu.1.2.part.1.name=sro_id_1@
qu.1.2.part.1.maple_answer=$ANS1@
qu.1.2.part.1.editing=useHTML@
qu.1.2.part.1.question=(Unset)@
qu.1.2.part.1.libname=@
qu.1.2.part.1.mode=Maple@
qu.1.2.part.1.allow2d=1@
qu.1.2.part.1.plot=@
qu.1.2.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.2.part.1.type=formula@
qu.1.2.part.2.name=sro_id_2@
qu.1.2.part.2.maple_answer=$ANS2@
qu.1.2.part.2.editing=useHTML@
qu.1.2.part.2.question=(Unset)@
qu.1.2.part.2.libname=@
qu.1.2.part.2.mode=Maple@
qu.1.2.part.2.allow2d=1@
qu.1.2.part.2.plot=@
qu.1.2.part.2.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.2.part.2.type=formula@
qu.1.2.part.3.name=sro_id_3@
qu.1.2.part.3.maple_answer=$ANS3@
qu.1.2.part.3.editing=useHTML@
qu.1.2.part.3.question=(Unset)@
qu.1.2.part.3.libname=@
qu.1.2.part.3.mode=Maple@
qu.1.2.part.3.allow2d=1@
qu.1.2.part.3.plot=@
qu.1.2.part.3.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.2.part.3.type=formula@
qu.1.2.question=<p>Use the closed form formulas to evaluate the following series:</p><p>(i) <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>$picka</mi></mrow></munderover><mi>n</mi></mrow></mstyle></math> = <span>&nbsp;</span><1><span>&nbsp;</span></p><p><span>(ii) <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>$picka</mi></mrow></munderover><mi>$pickc</mi></mrow></mstyle></math></span> = <span>&nbsp;</span><2><span>&nbsp;</span></p><p><span>(iii) <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>$picke</mi></mrow></munderover><mfenced open='(' close=')' separators=','><mrow><msup><mi>$d</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>$d</mi><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math></span> = <span>&nbsp;</span><3><span>&nbsp;</span></p><p><span><p><span>For (iii) you do not have to simplify the exponents in the answer. (i.e., You could enter 5^8 instead of 390625).</span></p></span></p>@

qu.1.3.mode=Inline@
qu.1.3.name=Geometric Sequence i@
qu.1.3.comment=<p>Recall for an geometric sequence the general <em>n</em>'th term is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi>r</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msub><mi>X</mi><mrow><mn>1</mn></mrow></msub></mrow></mstyle></math></p>@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$a=[2,4];
$picka=switch(rint(2),$a);
$pickr=frac(1,$picka);
$b=[96,192,144];
$pickb=switch(rint(3),$b);
$func="x->($pickr)^(x-1)*$pickb";
$c=[4,5,6,7,8];
$pickc=switch(rint(5),$c);
$m = maple("
convert((($func)(2)) ,string),
convert((($func)(3)) ,string),
convert((($func)($pickc)) ,string)
");
$f=switch(0,$m);
$g=switch(1,$m);
$ANS=switch(2,$m);@
qu.1.3.uid=1810c51e-5921-480b-8d0c-0e58181aae18@
qu.1.3.info=  Author=Steve Crane, Gord Clement;
  Course=Introductory Calculus for the Biological Sciences;
  Topic=Sequences and Series;
  Sub-Topic=Geometric Series;
@
qu.1.3.weighting=1@
qu.1.3.numbering=alpha@
qu.1.3.part.1.name=sro_id_1@
qu.1.3.part.1.maple_answer=$ANS@
qu.1.3.part.1.editing=useHTML@
qu.1.3.part.1.question=(Unset)@
qu.1.3.part.1.libname=@
qu.1.3.part.1.mode=Maple@
qu.1.3.part.1.allow2d=1@
qu.1.3.part.1.plot=@
qu.1.3.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.3.part.1.type=formula@
qu.1.3.question=<p>If the sequence&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><munderover><mi></mi><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mi>&infin;</mi></mrow></mrow></munderover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='{' close='}' separators=','><mrow><mi>$pickb</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$f</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$g</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.0em'>..</mo><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mfenced></mrow></mstyle></math>, then&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>$pickc</mi></mrow></msub></mrow></mstyle></math>=</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.4.mode=Inline@
qu.1.4.name=Finite Series (Closed Form) ii@
qu.1.4.comment=<p>Recall the following closed form formulas</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>N</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>N</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><mi>g</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>r</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>g</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>r</mi><mrow><mi>N</mi></mrow></msup></mrow></mfenced></mrow><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>r</mi></mrow></mfrac></mrow></mstyle></math></p>
<p>&nbsp;</p>@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=$a=rint(2,6);
$b=rint(2,4);
condition: ne($a,$b);
$c="[20,30,40,50,60]";
$pickc=switch(rint(8),$c);
$d=$pickc+1;
$ANS1=($pickc)*($d)/2;
$e="[3,4,5,6,7]";
$picke=switch(rint(6),$e);
$f=rint(2,5);
$g=$picke+1;@
qu.1.4.uid=f412b46f-6485-492e-92a5-3c14bfd7fc86@
qu.1.4.weighting=1,1@
qu.1.4.numbering=alpha@
qu.1.4.part.1.name=sro_id_1@
qu.1.4.part.1.maple_answer=$ANS1@
qu.1.4.part.1.editing=useHTML@
qu.1.4.part.1.question=(Unset)@
qu.1.4.part.1.libname=@
qu.1.4.part.1.mode=Maple@
qu.1.4.part.1.allow2d=1@
qu.1.4.part.1.plot=@
qu.1.4.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.4.part.1.type=formula@
qu.1.4.part.2.name=sro_id_2@
qu.1.4.part.2.maple_answer=($f)*(1-(1/2)^$picke)/(1/2)@
qu.1.4.part.2.editing=useHTML@
qu.1.4.part.2.question=(Unset)@
qu.1.4.part.2.libname=@
qu.1.4.part.2.mode=Maple@
qu.1.4.part.2.allow2d=1@
qu.1.4.part.2.plot=@
qu.1.4.part.2.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.4.part.2.type=formula@
qu.1.4.question=<p>Use the closed form formulas to evaluate the following series:</p><p>(i) <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>$pickc</mi></mrow></munderover><mi>n</mi></mrow></mstyle></math> = <span>&nbsp;</span><1><span>&nbsp;</span></p><p><span>(ii) <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munderover><mo lspace='0.0em' rspace='0.1666667em' stretchy='true' largeop='true' movablelimits='true'>&Sum;</mo><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mi>$picke</mi></mrow></munderover><mi>$f</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math></span> = <span>&nbsp;</span><2></p>@

qu.1.5.mode=Inline@
qu.1.5.name=Geometric Sequence ii@
qu.1.5.comment=<p>Recall for an geometric sequence the general <em>n</em>'th term is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi>r</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msub><mi>X</mi><mrow><mn>1</mn></mrow></msub></mrow></mstyle></math></p>@
qu.1.5.editing=useHTML@
qu.1.5.solution=@
qu.1.5.algorithm=$a=[2,3,4];
$picka=switch(rint(3),$a);
$b=[2,3,5];
$pickb=switch(rint(3),$b);
$func="x->($picka)^(x-1)*$pickb";
$c=[4,5,6,7];
$pickc=switch(rint(4),$c);
$m = maple("
convert((($func)(2)) ,string),
convert((($func)(3)) ,string),
convert((($func)($pickc)) ,string)
");
$f=switch(0,$m);
$g=switch(1,$m);
$ANS=switch(2,$m);@
qu.1.5.uid=0e73866e-fbc2-44ab-b94b-e16b220f858e@
qu.1.5.info=  Author=Steve Crane, Gord Clement;
  Course=Introductory Calculus for the Biological Sciences;
  Topic=Sequences and Series;
  Sub-Topic=Geometric Sequence;
@
qu.1.5.weighting=1@
qu.1.5.numbering=alpha@
qu.1.5.part.1.name=sro_id_1@
qu.1.5.part.1.maple_answer=$ANS@
qu.1.5.part.1.editing=useHTML@
qu.1.5.part.1.question=(Unset)@
qu.1.5.part.1.libname=@
qu.1.5.part.1.mode=Maple@
qu.1.5.part.1.allow2d=1@
qu.1.5.part.1.plot=@
qu.1.5.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.5.part.1.type=formula@
qu.1.5.question=<p>If the sequence&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><munderover><mi></mi><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mi>&infin;</mi></mrow></mrow></munderover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='{' close='}' separators=','><mrow><mi>$pickb</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$f</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$g</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.0em'>..</mo><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mfenced></mrow></mstyle></math>, then&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>$pickc</mi></mrow></msub></mrow></mstyle></math>=</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.6.mode=Inline@
qu.1.6.name=Fibonacci@
qu.1.6.comment=<p>Recall that in a Fibonacci Sequence: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub></mrow></mstyle></math> are specified and</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>f</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>2</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>f</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>f</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>for <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>2</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>3</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.2222222em' rspace='0.0em'>..</mo><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mstyle></math></p>@
qu.1.6.editing=useHTML@
qu.1.6.solution=@
qu.1.6.algorithm=$a=rint(2,7);
$b=rint(2,7);
condition: ge($b,$a) ne($a,$b);
$m=maple("
f:=proc(n)
 option remember:
 if n=1 then $a:
 elif n=2 then $b:
 else thisproc(n-1) + thisproc(n-2):
 end if:
end proc:
convert(f(6),string),
convert(f(8), string),
convert(f(1),string)");
$g=switch(0,$m);
$h=switch(1,$m);
$ANS=switch(2,$m);@
qu.1.6.uid=03c2a444-3bd4-4a11-9cd4-327a96eed8f8@
qu.1.6.info=  Author=Steve Crane, Gord Clement;
  Course=Introductory Calculus for the Biological Sciences;
  Topic=Sequences and Series;
  Sub-Topic=Fibonacci;
@
qu.1.6.weighting=1@
qu.1.6.numbering=alpha@
qu.1.6.part.1.name=sro_id_1@
qu.1.6.part.1.maple_answer=$ANS@
qu.1.6.part.1.editing=useHTML@
qu.1.6.part.1.question=(Unset)@
qu.1.6.part.1.libname=@
qu.1.6.part.1.mode=Maple@
qu.1.6.part.1.allow2d=1@
qu.1.6.part.1.plot=@
qu.1.6.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.6.part.1.type=formula@
qu.1.6.question=<p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msubsup><mfenced open='{' close='}' separators=','><mrow><msub><mi>f</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mi>&infin;</mi></mrow></mrow></msubsup></mrow></mstyle></math>is a Fibonacci sequence and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>f</mi><mrow><mn>6</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$g</mi></mrow></mstyle></math>and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>f</mi><mrow><mn>8</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$h</mi></mrow></mstyle></math>then&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math></p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.7.mode=Inline@
qu.1.7.name=Arithmetic Sequence ii@
qu.1.7.comment=<p>Recall for an arithmetic sequence the general <em>n</em>'th term is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>X</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfenced open='(' close=')' separators=','><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>d</mi></mrow></mstyle></math></p>@
qu.1.7.editing=useHTML@
qu.1.7.solution=@
qu.1.7.algorithm=$a=[2,3,4,5];
$picka=switch(rint(4),$a);
$b=[3,4,5,6,7];
$pickb=switch(rint(5),$b);
$func="x->$picka+(x-1)*$pickb";
$c=[45,46,47,48,49,50,51,52,53,54,55];
$pickc=switch(rint(12),$c);
$m=maple("
(($func)(2)),
(($func)(3)),
(($func)($pickc))
");
$f=switch(0,$m);
$g=switch(1,$m);
$ANS=switch(2,$m);@
qu.1.7.uid=738b12e1-46c9-4303-aa22-b7cc16e1dbdc@
qu.1.7.info=  Author=Steve Crane, Gord Clement;
  Course=Introductory Calculus for the Biological Sciences;
  Topic=Sequences and Series;
  Sub-Topic=Arithmetic Sequence;
@
qu.1.7.weighting=1@
qu.1.7.numbering=alpha@
qu.1.7.part.1.name=sro_id_1@
qu.1.7.part.1.maple_answer=$ANS@
qu.1.7.part.1.editing=useHTML@
qu.1.7.part.1.question=(Unset)@
qu.1.7.part.1.libname=@
qu.1.7.part.1.mode=Maple@
qu.1.7.part.1.allow2d=1@
qu.1.7.part.1.plot=@
qu.1.7.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.7.part.1.type=formula@
qu.1.7.question=<p>If the sequence&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><munderover><mi></mi><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mi>&infin;</mi></mrow></mrow></munderover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='{' close='}' separators=','><mrow><mi>$picka</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$f</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$g</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.0em'>..</mo><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mfenced></mrow></mstyle></math>, then&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>$pickc</mi></mrow></msub></mrow></mstyle></math>=</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.8.mode=Inline@
qu.1.8.name=Arithmetic Sequence i@
qu.1.8.comment=<p>Recall for an arithmetic sequence the general <em>n</em>'th term is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>a</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>a</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfenced open='(' close=')' separators=','><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>d</mi></mrow></mstyle></math></p>@
qu.1.8.editing=useHTML@
qu.1.8.solution=@
qu.1.8.algorithm=$a=[2,4,6,8];
$picka=switch(rint(8),$a);
$b=[2,4,6,8,12];
$pickb=switch(rint(5),$b);
$func="x->$picka+(x-1)*$pickb";
$m = maple("
convert((($func)(5)) ,string),
convert(((($func)(12)-($func)(8))) ,string)
");
$f=switch(0,$m);
$g=switch(1,$m);@
qu.1.8.uid=1841be69-4667-458b-8f86-a553e2ed878b@
qu.1.8.weighting=1@
qu.1.8.numbering=alpha@
qu.1.8.part.1.name=sro_id_1@
qu.1.8.part.1.maple_answer=$picka@
qu.1.8.part.1.editing=useHTML@
qu.1.8.part.1.question=(Unset)@
qu.1.8.part.1.libname=@
qu.1.8.part.1.mode=Maple@
qu.1.8.part.1.allow2d=1@
qu.1.8.part.1.plot=@
qu.1.8.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.8.part.1.type=formula@
qu.1.8.question=<p>If, in an arithmetic sequence <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><msub><mi>a</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced><munderover><mi></mi><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo></mrow></munderover><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msub><mi>a</mi><mrow><mn>5</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$f</mi></mrow></mstyle></math>and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>a</mi><mrow><mn>12</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msub><mi>a</mi><mrow><mn>8</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$g</mi></mrow></mstyle></math> then&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>a</mi><mrow><mn>1</mn></mrow></msub></mrow></mstyle></math>equals.</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.9.mode=Inline@
qu.1.9.name=Geometric Sequence iii@
qu.1.9.comment=<p>Recall for an geometric sequence the general <em>n</em>'th term is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>g</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>g</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>r</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msup></mrow></mstyle></math></p>@
qu.1.9.editing=useHTML@
qu.1.9.solution=@
qu.1.9.algorithm=$a=[2,3,4];
$picka=switch(rint(5),$a);
$b=[4,6,8];
$pickb=switch(rint(6),$b);
$func="x->($picka)^(x-1)*$pickb";
$c=[4,5,6,7];
$pickc=switch(rint(4),$c);
$m = maple("
convert((($func)(2)) ,string),
convert((($func)(3)) ,string),
convert((($func)($pickc)) , string)
");
$f=switch(0,$m);
$g=switch(1,$m);
$ANS=switch(2,$m);@
qu.1.9.uid=67321dc6-737a-46e2-ab42-e1f1194ebd8c@
qu.1.9.info=  Author=Steve Crane, Gord Clement;
  Course=Introductory Calculus for the Biological Sciences;
  Topic=Sequences and Series;
  Sub-Topic=Geometric sequence;
@
qu.1.9.weighting=1@
qu.1.9.numbering=alpha@
qu.1.9.part.1.name=sro_id_1@
qu.1.9.part.1.maple_answer=$ANS@
qu.1.9.part.1.editing=useHTML@
qu.1.9.part.1.question=(Unset)@
qu.1.9.part.1.libname=@
qu.1.9.part.1.mode=Maple@
qu.1.9.part.1.allow2d=1@
qu.1.9.part.1.plot=@
qu.1.9.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.9.part.1.type=formula@
qu.1.9.question=<p>If the sequence&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><munderover><mi></mi><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mi>&infin;</mi></mrow></mrow></munderover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='{' close='}' separators=','><mrow><mi>$pickb</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$f</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>$g</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.0em'>..</mo><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mfenced></mrow></mstyle></math>, then&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>$pickc</mi></mrow></msub></mrow></mstyle></math>=</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

