Answer
An explicit rule for the sequence is
$a_n=-2(9)^{n-1}$
Work Step by Step
The given recursive rule is
$a_1=-2,a_n=9a_{n-1}$
First term is $a_1=-2$.
and common ratio $r=9$.
Explicit rule for an geometric sequence.
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $-2$ for $a_1$ and $9$ for $d$.
$\Rightarrow a_n=-2(9)^{n-1}$
