Suppose $\displaystyle x_1,x_2,x_3,\mbox{...},x_n$ are in Arithmetic Progression. It is given that $\displaystyle x_1 + x_2 + \mbox{...} + x_n = a$ and $\displaystyle x_1^2 + x_2^2 + \mbox{...} + x_n^2 = b^2$. Determine the progression.

Answer:Spoiler:

I was unable to do it. Any ideas?