Competition Series

Competition Maths Questions – Series and Sequences?

Hi all!
I’ve got some homework from a maths class which I attend that’s got me stumped. I know the basics about series and sequences, but I can’t seem to figure how to work these two questions out.
Full solutions would be helpful!
Question 1:
The sum of the first x terms of a particular sequence is given by an expression ax^2 + bx + c, where x is any positive integer and a, b and c are constants. Prove that the sequence is arithmetic.

Hint for Question 1:

If S(x) is the sum of the first x terms of a sequence, then the xth term is given by S(x) – S(x-1).

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