MCQ
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:
- A$2 - \sqrt 3 $
- ✓$2 + \surd 3$
- C$\sqrt 2 + \surd 3$
- D$3 + \surd 2$
If $a r$ is doubled then,
$\Longrightarrow 2 a r=\frac{a r^{2}+a}{2}$
$\Longrightarrow 4 a r=a r^{2}+a$
$\Longrightarrow 4 r=r^{2}+1$
$\Longrightarrow r^{2}-4 r+1$
On solving we get
$r=2 \pm \sqrt{3}$
since it is an increasing
$G . P^{\prime} r^{\prime}=2+\sqrt{3}$
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