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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 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 4
Let the total number of terms in G.P be 2n with first term A and common ratio R

then S2n=AR2n1R1

and sum of numbers occupying the odd places is:

Sn=AR2n1R21

in 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

AR2n1R1=5AR2n1R21 [Sum of GP =a(rn1)r1 when r>1]

1R1=5R21

R21R1=5

R+1=5

R=4

Hence the correct option is D

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