Three positive numbers form an increasing G . P . If the middle term in this G . P . is doubled, the new…

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 :
  1. 2 - 3
  2. 2 + 3
  3. 2 + 3
  4. 3 + 2

Solution

Let the three numbers of the GP be a, ar and ar2 where r is the common ratio.
According to the given condition, a, 2ar and ar2 are in AP.

∴  2ar=a+ar22

∴  a+ar2=4ar

∴  r2+1=4r

∴  r2-4r+1=0

∴  r=4±16-42

         = 4 ± 2 3 2 = 2 ± 3

As it is an 'increasing' GP, r > 1.

∴  r=2+3.

Asked in: JEE Main 2014 (06 Apr)

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