Question

The sum of three numbers in $A.P$ is $15$ and their product is $80$. Find the numbers.

Answer 1

Let the first term be $a$ and common difference be $d$.

The three terms are,

$a-d,a,a+d$

As, the sum of three terms is 15, then,

$a-d+a+a+d=15$

$3a=15$

$a=5$

As, the product of three terms is 80, then,

$\left(5-d\right)5\left(5+d\right)=80$

$5\left(25-d^2\right)=80$

$25-d^2=16$

$d^2=9$

$d=\pm 3$

The numbers are $2,5,8$ or $8,5,2$.