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+3
200
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1. What is the sum of the first 8 terms of the geometric series?

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

We are not here to do all your homework.

Multiple questions have been deleted.

Melody.

Jan 24, 2020
edited by Melody  Jan 24, 2020

#1
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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.

Jan 24, 2020