- What is the sum of the first 8 terms of the geometric series?

120-80+160/3-320/9+....

Express your answer as a simplified fraction.

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Melody.

Vanessadeirdre Jan 24, 2020

#1**+2 **

The common ratio r is \(-\frac{2}{3}\) How is it found? ----> \(\frac{a_2}{a_1}\) Since it is a geometric series.

This series is a finite (I.e. you just want the sum of the first 8 terms)

There is a formula for it which is:

\(S_n=\frac{a_1(1-r^n)}{1-r}\) , of course "r" can't be equal to 1

The first term we have is 120, common ratio is \(-\frac{2}{3}\) (r) and we want the sum of the first 8 terms so just substituting them will give you the answer.

\(\frac{120*(1-(-2/3)^8}{1-(-2/3)}\) Just simplify it.

Guest Jan 24, 2020