This would be better as "find the nth element of an array." Also, a column matrix doesn't exist. Perhaps you meant column vector, though the variables in your test cases are row vectors.
Sum all integers from 1 to 2^n
Project Euler: Problem 2, Sum of even Fibonacci
Perfect Square or not
Find remainder when x is divided by 3
multiply an array by its position number
find a specific element from an matrix
find the mean of all elements in a matrix
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