Answer
An explicit rule for the sequence is
$a_n=-12n+20$
Work Step by Step
The given recursive rule is
$a_1=8,a_n=a_{n-1}-12$
First term is $a_1=8$.
and common difference $d=-12$.
Explicit rule for an arithmetic sequence.
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $8$ for $a_1$ and $-12$ for $d$.
$\Rightarrow a_n=8+(n-1)(-12)$
Use distributive property.
$\Rightarrow a_n=8-12n+12$
Simplify.
$\Rightarrow a_n=-12n+20$
