Verified Solution • 2025–26 Session moderate

QJEEM14Ma75c3: JEE Main 2014 Mathematics - Class 11 JEEM14Ma75c3 Solution: Three positive numbers form an increasing G.P. If the middle…

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 :

Multiple Choice Options

  • A 2−32 - \sqrt 3
  • B 2+32 + \sqrt 3
  • C 2+3\sqrt 2 + \sqrt 3
  • D 3+23 + \sqrt 2

Step-by-Step Verified Solution

Let a,ar,ar2a,ar,a{r^2} are in G.P.G.P.

According to the question

a,2ar,ar2a,2ar,a{r^2} are in A.P.A.P.

⇒2×2ar=a+ar2\Rightarrow 2 \times 2ar = a + a{r^2}

⇒4r=1+r2\Rightarrow 4r = 1 + {r^2}

⇒r2−4r+1=0\Rightarrow {r^2} - 4r + 1 = 0

r=4±16−42=2±3r = {{4 \pm \sqrt {16 - 4} } \over 2} = 2 \pm \sqrt 3

Since r > 1

∴\therefore π=2−3\pi = 2 - \sqrt 3 is rejected

Hence, r=2+3r = 2 + \sqrt 3

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