A gp consists of an even number of terms

Asked by admin @ 12/08/2021 in Math viewed by 278 People

A G.P. consists of an even number of terms.if the sum of all the terms is 3 times the sum of the odd terms ,then find its common ratio.

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Answered by admin @ 12/08/2021

Let the sequence be $a, ar^2, ar^3, ar^4,.........$

Sum of terms in odd positions = $\frac{a(r^{2n}-1)}{r^{2}-1}$ = m (say)

Sum of terms in even position = $\frac{ar(r^{2n}-1)}{r^{2}-1}$ = n (say)

Sum of all the terms in sequence = $m+n = 3m$

$\implies n=2m \\ \\ \frac{ar(r^{2n}-1)}{r^{2}-1} = 2\times \frac{a(r^{2n}-1)}{r^{2}-1} \\ \\ r=2$

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