If in an infinite G.P. first term is equal to twice of sum of remaining terms, then its common ratio

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8. Sequences and Series

easy

If in an infinite $G.P.$ first term is equal to the twice of the sum of the remaining terms, then its common ratio is

A

$1$

B

$2$

C

$1/3$

D

$-1/3$

Solution

(c) Given, $a = 2\left( {\frac{{ar}}{{1 – r}}} \right)$

$ \Rightarrow 1 – r = 2r$

$ \Rightarrow r = \frac{1}{3}$.

Standard 11

Mathematics

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