Question

If $a,2b,3c$ are in A.P. and $a,b,c$ are in G.P., then the common ratio of the G.P. is

• A. $1$
• B. $3$
• C. $\frac{1}{3}$
• D. $2$

Answer 1

Answer: (A), (C)

The correct options are
A $1$
C $\frac{1}{3}$

Given $a,b,c$ are in GP let the common ratio be $r$.

Therefore, $b=a.r,c=a.r^2$

Also, $a,2b,3c$ are in AP.

$\Rightarrow 2\left(2b\right)=4b=a+3c$

$\Rightarrow 4.a.r=a+3.a.r^2$

i.e. $3r^2-4.r+1=0$

$\Rightarrow r=1,\frac{1}{3}$