The sum of the first terms of an infinite sequence is for all .

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The sum of the first

n

terms of an infinite sequence is

\frac{3n^2 + 5n}{2}

for all

n \in \mathbb{Z}^+

. (1) Find the

n

th term. (2) Prove that the sequence is arithmetic.