Three-numbers-form-an-increasing-GP-If-the-middle-number-is-doubled-then-the-new-numbers-are-in-AP-The-common-ratio-of-the-GP-is-

Question Number 43628 by peter frank last updated on 12/Sep/18

Three numbers form an increasing GP .

If the middle number is doubled, then the

new numbers are in AP . The common ratio

of the GP is

Answered by $@ty@m last updated on 13/Sep/18

A T Q

\frac{a}{r}, 2 a, a r a r e i n A P

\Rightarrow 4 a = \frac{a}{r} + a r

\Rightarrow 4 = \frac{1}{r} + r

\Rightarrow 4 = \frac{1 + r^{2}}{r}

\Rightarrow r = 2 \pm \sqrt{3} A n s .

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