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Question

Three number are in G.P. If we double the middle term, we get an A.P. then the common ratio of  the G.P. is-.


A
2±3
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B
3±2
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C
3±5
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D
None of these
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Solution

The correct option is A $$2 \pm \sqrt 3 $$
If $$a,ar,{ar}^{2}$$ are in GP.
$$\therefore a,2ar,{ar}^{2}$$ are in AP.
$$\therefore 2(2ar)=a{r}^{2}+a$$
$$4ar=a({r}^{2}+1)$$
$${r}^{2}-4r+1=0$$
$$r=\cfrac{+4\pm\sqrt{16-4}}{2}=\cfrac{4\pm2\sqrt{3}}{2}=2\pm2\sqrt{3}$$

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