Question

I need help answering thisIf you can, simply show your work

Answer 1

we have that

To find the sum of the first Sn terms of a geometric sequence use the formula

$S_n=\frac{a_1\cdot(1-r^n)}{1-r}$

where

a1=120 -----> first term

n=8

Find out the common ratio r

we have

a1=120

a2=-80

a3=160/3

so

a3/a2=(160/3)/(-80)=-2/3

a2/a1=-80/120=-2/3

so

r=2/3

substitute given values in the formula

$S_8=\frac{120\cdot(1-(-\frac{2}{3}^8))}{1+\frac{2}{3}}$$S_8=\frac{120\cdot(1-\frac{256}{6,561}^{})}{\frac{5}{3}}$$\begin{gathered} S_8=72\cdot(\frac{6,305}{6,561}^{}) \\ S_8=\frac{453,960}{6,561}^{} \end{gathered}$

Simplify

S_8=50,440/729