Answer
A recursive rule for the sequence is
$a_1=1,a_n=-5 a_{n-1}$
Work Step by Step
The given explicit rule is
$a_n=(-5)^{n-1}$
$a_n=1(-5)^{n-1}$
First term is
$a_1=1$
Common ratio is
$r=-5$
Recursive equation for a geometric sequence.
$a_n=r\cdot a_{n-1}$
Substitute $-5$ for $r$.
$a_n=-5\cdot a_{n-1}$
Hence, a recursive rule for the sequence is
$a_1=1,a_n=-5 a_{n-1}$
