Given an arithmetic progression -10,-5,0,........State three consecutive terms in this progression whose sum is 90.
You know that the difference $\displaystyle d = 5$.
Your three terms are therefore $\displaystyle x, x + 5, x + 10$.
You know they add up to $\displaystyle 90$.
So $\displaystyle x + x + 5 + x + 10 = 90$
$\displaystyle 3x + 15 = 90$
$\displaystyle 3x = 75$
$\displaystyle x = 25$.
So your three numbers are $\displaystyle 25, 30, 35$.
sum of n terms of A.P is given by
(n/2)(2A+(n-1)d)
here n= number of terms
A= first term
d= common difference
in given problem
n=3,d=5 so putting in equation we get
(3/2)(2A+10)=90
2A+10=60
A=25
since first term is A=25 other terms will be 30 and 35
so three terms are 25,30,35