Answer
An explicit rule for the sequence is
$ a_n=3n-6$
Work Step by Step
The given recursive rule is
$a_1=-3,a_n=a_{n-1}+3$
First term is $a_1=-3$.
and common difference $d=3$.
Explicit rule for an arithmetic sequence.
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $-3$ for $a_1$ and $3$ for $d$.
$\Rightarrow a_n=-3+(n-1)3$
Use distributive property.
$\Rightarrow a_n=-3+3n-3$
Simplify.
$\Rightarrow a_n=3n-6$
