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AM,GM,HM Inequality

Find Sn, th...

Question

Find $S_{n}$ , the sum of the first $n$ terms, for the following geometric series. $a_{1} = 120, a_{5} = 1, r = - 2$ .

20.66

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40.66

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80.66

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100.66

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Solution

The correct option is B $40.66$
Given, first term, $a = 120$ , common ratio, $r = - 2$ and $a_{5} = 1$
We know $S_{n} = \frac{a_{1} - a_{n} r}{1 - r}$
$S_{n} = \frac{120 - (- 2)}{1 - (- 2)}$
$S_{n} = \frac{120 - (- 2)}{1 - (- 2)}$
$S_{n} = \frac{122}{3}$
$S_{n} = 40.66$

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