Answer
Recursive formula: $a_{1}=-5$, $a_{n}=a_{n-1}+1.5$
Explicit formula: $a_{n}=1.5n-6.5$
Work Step by Step
The first term is $-5$ and the common difference is $-3.5-(-5)=-3.5+5=1.5$.
$\text{Explicit formula}$:
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:
$a_{n}=-5+(n-1)(1.5)$
$a_{n}=-5+(1.5n-1.5)$
$a_{n}=1.5n-6.5$
$Recursive formula$:
The recursive formula is $a_{n}=a_{n-1}+d$.
Substitute the value of $d$ to obtain:
$a_{n}=a_{n-1}+1.5$ where $a_1=-5$