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. $2\pm \sqrt{3}$
• B. $3\pm \sqrt{2}$
• C. $3\pm \sqrt{5}$
• D. None of these

Answer 1

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.

$\therefore 2\left(2ar\right)=a{r}^2+a$

$4ar=a(r^2+1)$

$r^2-4r+1=0$

$r=\frac{+4\pm \sqrt{16-4}}{2}=\frac{4\pm 2\sqrt{3}}{2}=2\pm 2\sqrt{3}$