A G.P. consists of an even number of terms. If sum of all terms is 5 times sum of terms occupying od

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8. Sequences and Series

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A $G.P.$ consists of an even number of terms. If the sum of all the terms is $5$ times the sum of the terms occupying odd places, then the common ratio will be equal to

A

$2$

B

$3$

C

$4$

D

$5$

Solution

(c) Let there be $2n$ terms in the given $G.P.$ with first term $a$ and the common ratio $r$.

Then, $a\frac{{({r^{2n}} – 1)}}{{(r – 1)}} = 5a\frac{{({r^{2n}} – 1)}}{{({r^2} – 1)}}$

$ \Rightarrow $$r + 1 = 5$

$ \Rightarrow $$r = 4$.

Standard 11

Mathematics

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