At first, we must find the common ratio between each two consecutive terms
[tex]\begin{gathered} \frac{-32}{128}=-\frac{1}{4} \\ \frac{8}{-32}=-\frac{1}{4} \end{gathered}[/tex]The common ratio is -1/4
The first term is 128
Then the recursive formula is
[tex]a_1=1stterm;a_n=r.a_{n-1}[/tex]r is the common ratio
r = -1/4
[tex]a_1=128;a_n=(-\frac{1}{4}).a_{n-1}[/tex]