Question

I need help solving this practice problem, I need it answered simply step by step

Answer 1

50440/729

Step-by-step explanation:

The sum of the first n terms of the geometric series is calculated as:

`S_n=(a(r^n-1))/(r-1)`

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

`-(80)/(120)=-(2)/(3)`

Therefore, replacing a by 120, r by -2/3, and n by 8, we get:

`\begin{gathered} S_n=(120((-2/3)^8-1))/((-2/3-1)) \\ S_n=(50440)/(729) \end{gathered}`

Then, the answer is 50440/729