Question

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

• A. $1,5,7$
• B. $2,6,8$
• C. $2,8,14$
• D. $4,8,10$

Answer 1

Answer: (C)

Let the three numbers be $a-d,a,a+d(d>0)$
Now $(a-d)a(a+d)=224$
$\Rightarrow a(a^2-d^2)=224...(i)$
Also, $a+d=7(a-d)$
$\Rightarrow d=\frac{3a}{4}$
Substituting this value of $d$ in $(i)$, we get
$a\left(a^2-\frac{9a^2}{16}\right)=224$
$\Rightarrow a=8$
and $d=\frac{3}{4}\times 8=6$
Hence, the three numbers are $2,8,14$.