Answer
A recursive rule for the sequence is
$a_1=5,a_n=-4a_{n-1}$
Work Step by Step
The given sequence is
$5,-20,80,-320,1280,...$
The first term is $a_1=5$.
Calculate ratio between each pair of consecutive terms.
$\frac{-20}{5}=-4$
$\frac{80}{-20}=-4$
$\frac{-320}{80}=-4$
$\frac{1280}{-320}=-4$
The common ratio is $d=-4$.
So, the sequence is geometric.
Recursive equation for a geometric sequence.
$a_n=r\cdot a_{n-1}$
Substitute $-4$ for $r$.
$a_n=-4a_{n-1}$
Hence, a recursive rule for the sequence is $a_1=5,a_n=-4a_{n-1}$
