Question

Which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an = 5+ (n-1)2?

Answer 1

`a_1 = 5`

`a_n = a_(n-1) + 2`

Explanation:

Given

`a_n = 5 + (n - 1)2`

Required

The equivalent recursive function

The general explicit function is:

`a_n = a_1+ (n - 1)d`

So, by comparison

`a_1 = 5`

`d = 2`

The recursion of an arithmetic sequence is:

`a_n = a_(n-1) + d`

Substitute 2 for d

`a_n = a_(n-1) + 2`

Hence: (a) is correct