Three positive numbers form an increasing GP. If the middle term of the GP is doubled, then new numbers are in AP. Then, the common ratio of the GP 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 the numbers in GP be a,ar,ar2.
If the middle term of the GP is doubled, then the new numbers are in AP. ⇒a,2ar,ar2 are in AP. ⇒4ar=a+ar2 ⇒r2−4r+1=0(∵a is positive) ⇒r=2±√3
Since the GP is increasing, we must have r=2+√3.