Question

# 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, the common ratio will be

A
2
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B
5
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C
3
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D
4
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Solution

## The correct option is D 4Let the total number of terms in G.P be 2n with first term A and common ratio Rthen S2n=AR2n−1R−1and sum of numbers occupying the odd places is:Sn=AR2n−1R2−1in this case, the first term which is at the 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 AR2 So,S2n=5Sn⇒AR2n−1R−1=5AR2n−1R2−1 [Sum of GP =a(rn−1)r−1 when r>1]⇒1R−1=5R2−1⇒R2−1R−1=5⇒R+1=5⇒R=4Hence the correct option is D

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