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  4. The sum of first 10 terms of a G.P. is equal to 244 times the sum of first five terms. Then the common ratio is

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Q. The sum of first 10 terms of a G.P. is equal to 244 times the sum of first five terms. Then the common ratio is

Sequences and Series

Solution:

$S_{10} = 244 $
$ S_{5}\Rightarrow \frac{a\left(1-r^{10}\right)}{1-r} = 244 a\frac{\left(1-r^{5}\right)}{1-r} $
$ \Rightarrow 1-r^{10} = 244 \left(1-r^{5}\right) $
$ \Rightarrow \left(1-r^{5}\right)\left(1+r^{5}\right) = 244\left(1-r^{5}\right)$
$ \Rightarrow 1+r^{5}= 244$
$ \Rightarrow r^{5} = 243 = \left(3\right)^{5} $
$\Rightarrow r=3$