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  4. The ratio of sum of first three terms of a G.P. to the sum of first six terms is 64: 91, the common ratio of GP. is

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Q. The ratio of sum of first three terms of a $G.P$. to the sum of first six terms is $64 : 91$, the common ratio of $GP$. is

Sequences and Series

Solution:

Given, $\frac{S_{3}}{S_{6}} = \frac{64}{91} = \frac{a \left(r^{3} - 1\right)}{a \left(r^{6} - 1\right)}$
$\Rightarrow \frac{\left(r^{3} -1 \right)}{\left(r^{3} + 1\right) \left(r^{3} - 1\right)} = \frac{64}{91}$
$\Rightarrow r^{3} = \frac{27}{64} \therefore r = \frac{3}{4}$