recall, a geometric series has this form with constants A for n=0, and k, the ratio of two consecutive terms n/(n+1)
[tex]
a_n =A*k^n[/tex]
you are given two values, for n=13 and n=10, put both into the equation
[tex]9=A*k^{10}[/tex]
[tex]-72=A*k^{13}[/tex]
Two equations with two unknown values A and k, you can solve for those.
Solving both for A,
[tex]A= \frac{9}{k^{10}} = \frac{-72}{k^{13}} [/tex]
[tex]k=-2
[/tex]
[tex]A= \frac{9}{1024} [/tex]
The general equation for the series is then,
[tex]a_n= \frac{9}{1024}(-2)^n [/tex]
use n=7
