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Question

A G. P consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

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Solution

Let the number of terms be 2n.

Let a, ar, ar2, ......, ar2n1, be in G.P.

Then, S2n=a(r2n1)r1

Now, the number of odd terms = n and common ratio =r2

Sn=a[(r2)n1]r21=a(r2n1)r21

S2n=5.Sn [Given]

a(r2n1)r1=5a(r2n1)r21

r+1=5

r=51=4


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