A=(1  1)

     (1  0)
Determine the smallest natural number n such that the matrix A^n contains

an entry greater than 2019.

(I know the answer is A^17, but I don't know how to use maple in order to determine when an entry becomes greater than 2019.)

Suppose that (x1, x2, . . . , xn) is a sequence of real numbers. The mean μ and the standard deviation σ are defined as
μ= n(x1 +x2 +...+xn);

σ=√[(1/2)n[(x1 −μ) +(x2 −μ) +...+(xn −μ) ]]

1. Suppose that n = 20 and xk = k for all k. Write for loops to determine the mean and the standard deviation of the sequence.

2. Suppose that n = 30 and xk = k3 for all k. Write for loops to determine the mean and the standard deviation of the sequence.