Answer:
50440/729
Explanation:
The sum of the first n terms of the geometric series is calculated as:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Where a is the initial term and r is the ratio.
To find the ratio, we need to divide the second term by the first one as follows
[tex]-\frac{80}{120}=-\frac{2}{3}[/tex]
Therefore, replacing a by 120, r by -2/3, and n by 8, we get:
[tex]\begin{gathered} S_n=\frac{120((-2/3)^8-1)}{(-2/3-1)} \\ S_n=\frac{50440}{729} \end{gathered}[/tex]
Then, the answer is 50440/729
