Three positive numbers form an increasing G.P. If the middle term in this G.P is doubled, then new numbers are in A.P. Then, the common ratio of the G.P. is
A
√2+√3
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B
3+√2
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C
2−√3
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D
2+√3
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Solution
The correct option is D2+√3 Let a,ar,ar2 are in GP, where (r > 1) On multiplying middle term by 2, we have a,2ar,ar2 are in an AP ⇒4ar=a+ar2 ⇒r2−4r+1=0 ⇒r=4±√16−42 =2±√3 ⇒r=2+√3 [since, AP is increasing]