JEE-Mains 2014 (9/30)

Algebra Level 3

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 :

Details and Assumptions :

A.P denotes an arithmetic progression.
G.P denotes a geometric progression.

3+\sqrt{2}

2-\sqrt{3}

\sqrt{2}+\sqrt{3}

2+\sqrt{3}

1 solution

Akshat Sharda
Jan 9, 2017

Let the 3 numbers be $a,ar,ar^2$ where $r$ is the common ratio and $r>1$ . Now $a,2ar,ar^2$ are in arithmetic progression.

$2(2ar)=a+ar^2 \Rightarrow \boxed{r=2+\sqrt{3}}$

JEE-Mains 2014 (9/30)

1 solution

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