Question

What is the recursive formula for the perimeter of a square of side n(the nth perimeter) using the first number(perimeter) in the pattern?

Answer 1

`a_n=a_(n-1)+4\qquad a_1=4`

Explanation:

You want the recursive formula that matches the sequence 4, 8, 12, 16, 20.

Recursive formula

Your problem statement tells you the recursive formula is ...

`a_n=a_(n-1)+d\qquad a_1=\text{first term}`

where 'd' is the common difference.

This means you only need to identify the perimeter associated with n=1 (first term), and the difference between perimeters for adjacent values of n.

The table tells you ...

`a_1=4\\d=8-4=4`

Filling these values into the given formula, you have the recursive formula ...

`\boxed{a_n=a_(n-1)+4\qquad a_1=4}`