Question

If $p,q$ and $r$ are in one geometric progression and $a,b,c$ in another geometric progression, then $cp,bq,ar$ are in

• A. $A.P$
• B. $H.P$
• C. $G.P$
• D. None of these

Answer 1

The correct option is C

$G.P$

Explanation for correct option

$p,q$ and $r$ are in GP

Then common ratio of $p,q$and $r$ is $R_1$

$q=R_{1}p$ as a result.

Therefore,$r={R_1}^{2}p$

$a,b,c$ are in GP

The common ratio of $a,b$, and $c$ is $R_2$.

$b=R_{2}a$ as a result.

Similarly, $c={R_2}^{2}a$

$bq=R_1{R}_{2}ap$

$cr={\left(R_1{R}_2\right)}^{2}ap$

As a result, $ap$, $bq$, and $cr$ are now in GP.

Hence option ‘c’ is correct.