Question

Find three numbers in AP whose sum is $21$ and their product is $336$.

• A. $6,7,8$
• B. $5,8,10$
  
• C. $6,9,12$
  
• D. None of these
  

Answer 1

Answer: (A)

$6,7,8$

Let the terms be $a-d,a,a+d$
Given, $(a+d)+a+(a-d)=21$
$\therefore 3a=21$
$\therefore a=7$
Also given, $(a+d)\left(a\right)(a-d)=336$
$\therefore 7(7^2-d^2)=336$
$\therefore 49-d^2=48$
$\therefore d^2=1$
$\therefore d=\pm 1$
For $d=1$ terms are $6,7,8$
For $d=-1$ terms are $8,7,6$