Answer:
[tex]a_n=a_{n-1}+4\qquad a_1=4[/tex]
Step-by-step 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 ...
[tex]a_n=a_{n-1}+d\qquad a_1=\text{first term}[/tex]
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 ...
[tex]a_1=4\\d=8-4=4[/tex]
Filling these values into the given formula, you have the recursive formula ...
[tex]\boxed{a_n=a_{n-1}+4\qquad a_1=4}[/tex]
