Question

find three numbers a,b,c which are in arithematic progression, between 2 and 18 such that their sum is 25

Answer 1

Let $a=3$
$3,b,c$ are in AP, so $b-3=c-b\implies c=2b-3$

$a+b+c=25$
substituting $a=3$ and $c=2b-3$ 
$3+b+2b-3=25$
$b=\frac{25}{3}$
$\implies c=\frac{41}{3}$

Thus the required numbers are $3,~\frac{25}{3},~\frac{41}{3}$