Question

The sum of three numbers in A.P is $27$. Their product is is $405$. Find the numbers.

Answer 1

Let the three numbers in $A.P$ is $a-d,a,a+d$

Sum of three numbers is $27$

$⟹a-d+a+a+d=27⟹a=9$

Product is $405$

$⟹(9-d)\left(9\right)(9+d)=405$

$⟹81-d^2=45⟹d^2=36⟹d=\pm 6$

The numbers are $3,9,15$