Three positive numbers form 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…

Question

Three positive numbers form 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 :

MARKS Content Team · Accepted Answer

Correct answer: (B) 2 + √3. Let the three numbers of the GP be a, ar and ar^2 where r is the common ratio. According to the given condition, a, 2ar and ar^2 are in AP. ∴ 2ar=(a+ar^2)/2 ∴ a+ar^2=4ar ∴ r^2+1=4r ∴ r^2-4r+1=0 ∴ r=(4±√(16-4))/2 = (4 ± 2 √3)/2 = 2 ± √3 As it is an 'increasing' GP, r > 1. ∴ r=2+√3.

Three positive numbers form 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 :

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