Answer
Recursive formula: $a_{1}=-32$, $a_{n}=a_{n-1}+12$
Explicit formula: $a_{n}=12n-44$
Work Step by Step
The first term is $-32$ and the common difference is $-20-(-32)=-20+32=12$.
$\text{Explicit formula}$:
The explicit formula is $a_{n}=a_{1}+(n-1)d$ where $a_1$=first term and $d$=common difference. Substitute the values of the common difference and the first term to obtain:
$a_{n}=-32+(n-1)(12)$
$a_{n}=-32+(12n-12)$
$a_{n}=12n-44$
$Recursive formula$:
The recursive formula is $a_{n}=a_{n-1}+d$.
Substitute the value of $d$ to obtain:
$a_{n}=a_{n-1}+12$ where $a_1=-32$
