Answer
A recursive rule for the sequence is
$a_1=-1,a_n=4a_{n-1}$
Work Step by Step
The given sequence is
$-1,-4,-16,-64,...$
The first term is $a_1=-1$.
Calculate ratio between each pair of consecutive terms.
$\frac{-4}{-1}=4$
$\frac{-16}{-4}=4$
$\frac{-64}{-16}=4$
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 $a_1=-1,a_n=4a_{n-1}$
