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Sum of Infinite Terms of a GP

The sum of in...

Question

The sum of infinite GP whose common ratio $r = \frac{2}{7}$ is $35$
Find the series .

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Solution

$r = \frac{2}{7}$
The sum of infinite GP is $\frac{a}{1 - r} = 35 \frac{a}{1 - \frac{2}{7}} = 35 \frac{a}{5} = \frac{35}{7} a = 25$
So the series is $25, \frac{50}{7}, \frac{100}{49}, . . .$

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