Find three numbers in AP whose sum is 15 and product is 80.

The correct answer is 2,5,8

Let the first term be $a$ and common difference be $d$.
So the three terms are $a−d$,$a$, $a+d$
As, the sum of three terms is 15, $ (a−d)+a+(a+d)=15$
∴ $3a=15$ or $a=5$

As, the product of three terms is 80, $(5−d)5(5+d)=80$
⇒ $5(25−d^2 )=80$
$25−d^2 = 16$ or $ d^2 = 9$
$d=±3$ So, the numbers are 2,5,8 or 8,5,2.