Answer
An explicit rule for the sequence is
$ a_n=20n-65$
Work Step by Step
The given recursive rule is
$a_1=-45,a_n=a_{n-1}+20$
First term is $a_1=-45$.
and common difference $d=20$.
Explicit rule for an arithmetic sequence.
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $-45$ for $a_1$ and $20$ for $d$.
$\Rightarrow a_n=-45+(n-1)20$
Use distributive property.
$\Rightarrow a_n=-45+20n-20$
Simplify.
$\Rightarrow a_n=20n-65$
