Question

The product of three numbers in A.P. is $224$ , and the largest number is $7$ times the smallest .Find the numbers.

Answer 1

Let $3$ numbers be $a-d,a,a+d$

Now, $a+d=7(a-d)......\left(i\right)$
$\Rightarrow 6a=8d......\left(ii\right)$
$\&(a-d)\left(a\right)(a+d)=224$
$\Rightarrow \left(\frac{4d}{3}\right)\left(\frac{7d}{3}\right)\left(\frac{d}{3}\right)=\mathrm{224.........}from\left(i\right)and\left(ii\right)$
$\Rightarrow d=6,a=8$

$\therefore$ Numbers are $2,8,14$