Let be a positive integer.

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

Problem

Let

n

be a positive integer. (a) Evaluate

\displaystyle S_n=\sum_{k=1}^{n}(4k-3)+5\sum_{k=1}^{n}2

and express the answer in its simplest form in terms of

n

. (b) Hence find

S_{20}

. (Leave the final answer as an integer.)