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Question

Three positive numbers from an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is:

A
23
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B
2+3
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C
2+3
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D
3+2
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Solution

The correct option is B 2+3
Let a,ar,ar2 are in G.P.
According to the question
a, 2ar, ar2 are in A.P.
2×2ar=a+ar2
4r=1+r2r24r+1=0
r=4±1642=2±3
Since r > 1
r=23 rejected
Hence, r=2+3

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