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

Engineering

Mathematics

Geometric Progression and Its Properties

Question

$3 + \sqrt{2}$

$2 - \sqrt{3}$

$\sqrt{2} + \sqrt{3}$

$2 + \sqrt{3}$

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Let 3 positive numbers in GP be

a, ar, ar² where r > 1

Now, a, 2ar, ar² are in AP

4ar = a + ar²

r² – 4r + 1 = 0

$r = \frac{4 \pm \sqrt{16 - 4}}{2}$

r = 2 ± $\sqrt{3}$ but r > 1

$∴ r = 2 + \sqrt{3}$