Question

The sum of four numbers in AP is $20.$ The numbers are such that the ratio of the product of first and fourth is to the product of second and third as $2:3.$ The greatest number is:-

• A. $8$
• B. $7$
• C. $14$
• D. $4$

Answer 1

The correct option is A $8$

Let the four terms be $a-3d,a-d,a+d,anda+3d$ with common difference $2d$.

$sum=4a=20$

$a=5$

$\frac{(a-3d)(a+3d)}{(a-d)(a+d)}=\frac{2}{3}$

$\frac{25-9d^2}{25-d^2}=\frac{2}{3}$

$d^2=1$$\Rightarrow d=1$

$Largestterm=a+3d$$=5+3\left(1\right)$$=8.$