calculus polynomial

Question

Find a closed form for the sequence of differences of an=an^2+bn+c. That is, prove that every quadratic sequence has arithmetic differences.

Answer 1

First of all, what you really mean is a_n = An² + Bn + C

When you write and simplify the expression for Δa_n you will get A(2n+1) + B...but you should do that algebra yourself to be sure that it is correct. Δa_n = a_n+1 - a_n