If ratio of sum of first three terms and sum of first six terms of a G.P. be 125 : 152 , then common

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8. Sequences and Series

easy

If the ratio of the sum of first three terms and the sum of first six terms of a $G.P.$ be $125 : 152$, then the common ratio r is

A

$\frac{3}{5}$

B

$\frac{5}{3}$

C

$\frac{2}{3}$

D

$\frac{3}{2}$

Solution

(a) Here $\frac{{{S_3}}}{{{S_6}}} = \frac{{125}}{{152}}$

$\Rightarrow \frac{{a({r^3} – 1)/(r – 1)}}{{a({r^6} – 1)/(r – 1)}} = \frac{{125}}{{152}}$

$ \Rightarrow $$({r^3} – 1)152 = 125({r^6} – 1) $

$\Rightarrow {r^3} = \frac{{27}}{{125}}$

$\Rightarrow r = \frac{3}{5}$.

Standard 11

Mathematics

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