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Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

A

`sqrt(2)+sqrt(3)`

B

`3+sqrt(2)`

C

`2- sqrt(3)`

D

` 2+sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
d
Let a,ar,`ar^(2)` be in GP `(r gt 1)`
On multiplying middle term by 2 , then a, 2ar , `ar^(2)` are in AP.
` rArr 4ar = a+ ar^(2)`
` rArr r^(2) - 4r +1 = 0 ` ,brgt ` rArr r = (4pmsqrt(16-4))/2 = 2 pm sqrt(3)`
` rArr r = 2 + sqrt(3) " " [ :' "AP is increasing"]`
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Knowledge Check

  • Three positive numbers form an increasing GP. If the middle terms in this GP is doubled, the new numbers are in AP. Then, the common ratio of the GP is

    A
    `2-sqrt(3)`
    B
    `2+sqrt(3)`
    C
    `sqrt(2)+sqrt(3)`
    D
    `3+sqrt(2)`

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    A
    `sqrt(2)+sqrt(3)`
    B
    `3+sqrt(2)`
    C
    `2-sqrt(3)`
    D
    `2+sqrt(3)`

  • Three numbers form an increasing G.P. . If the middle number id doubled, then the new numbers are in A.P. The common ratio of the G.P is:

    A
    a)`2-sqrt3`
    B
    b)`2+sqrt3`
    C
    c)`sqrt3-2`
    D
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