Question

The sum of the three numbers which are in arithmetic progression is $12$. If the third number is three times the first number, than the product of the numbers is

• A. $32$
• B. $40$
• C. $24$
• D. $48$

Answer 1

The correct option is D $48$

Let the 3 no in A.P be : $a-d,a,a+d$

$\therefore$ Sum of these number $=(a-d)+\left(a\right)+a+d$

$12=3a$

$4=a$

and also

$a+d=3(a-d)$

$a+d=3a-3d$

$4d=2a$

$2d=a$

$d=4/2=2$

$d=2$

$\therefore A.P\Rightarrow a-d,a,a+d$

$\Rightarrow 4-2,4,4+2$

$\Rightarrow 2,4,6.$

$\therefore$ product $\Rightarrow 2\times 4\times 6$

$\Rightarrow 48$ (option D)