Answer
A recursive rule for the sequence is
$a_1=-81,a_n=\frac{2}{3}a_{n-1}$
Work Step by Step
The given explicit rule is
$a_n=-81(\frac{2}{3})^{n-1}$
First term is
$a_1=-81$
Common ratio is
$r=\frac{2}{3}$
Recursive equation for a geometric sequence.
$a_n=r\cdot a_{n-1}$
Substitute $\frac{2}{3}$ for $r$.
$a_n=\frac{2}{3}\cdot a_{n-1}$
Hence, a recursive rule for the sequence is
$a_1=-81,a_n=\frac{2}{3}a_{n-1}$
