Question

What is the common difference of an AP in which the ratio of the product of the first and fourth term to the product of the second and third term is $2:3?$ It is given that the sum of the four terms is $20.$

• A. $3$
• B. $4$
• C. $1$
• D. $2$

Answer 1

The correct option is D $2$

Let the four terms be $a-3x,a-x,a+x,a+3x$
Sum $=4a=20$
$\Rightarrow a=5$
Ratio $=$ $\frac{(a-3x)\times (a+3x)}{(a-x)\times (a+x)}$ $=$ $\frac{2}{3}$
$3a^2-27x^2=2a^2-2x^2$
$a^2=25x^2$
$25=25x^2$
$x=1,-1$
Common difference $=2x=2$