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
B
3±2
C
3±5
D
None of these

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.$$\therefore 2(2ar)=a{r}^{2}+a$$$$4ar=a({r}^{2}+1)$$$${r}^{2}-4r+1=0$$$$r=\cfrac{+4\pm\sqrt{16-4}}{2}=\cfrac{4\pm2\sqrt{3}}{2}=2\pm2\sqrt{3}$$Maths

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