Question

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

Answer 1

Answer:

$a_1 = 5$

$a_n = a_{n-1} + 2$

Step-by-step 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