    Question

# A series in 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

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B

3

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C

4

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D

5

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Solution

## The correct option is A 4Let there be 2n terms in the given G.P. with first term a and the common ratio r.Then Sn=ar2n−1r−1In this case the first term which is at odd place will remain a but the common ratio will become r2 because the next term of the sequence will be at third position i.e. ar2So, now according to the question S2n=5Sn Then, a r2n−1(r−1) = 5a (r2n−1)(r2−1) ⇒1r−1=5r2−1⇒r2−1r−1=5⇒r+1=5⇒r=4  Suggest Corrections  22      Similar questions
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