Answer
Recursive formula: $a_{1}=-5$ ,$a_{n}=a_{n-1}+1$
Explicit formula: $a_{n}=n-6$
Work Step by Step
The sequence is $-5,-4,-3,-2,-1$.
The first term is $-5$ and the common difference is $-4-(-5)=-4+5=1$.
$\text{Explicit formula}$:
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:
$a_{n}=-5+(n-1)1$
$a_{n}=-5+n-1$
$a_{n}=n-6$
$\text{Recursive formula}$:
The recursive formula is $a_{n}=a_{n-1}+d$.
Substitute the value of $d$ to obtain:
$a_{n}=a_{n-1}+1$ where $a_1=-5$
