Consider the expression S_n = _ k=1 ^ n (6k+3)

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

Problem

Consider the expression

S_n = \sum_{k=1}^{n}(6k+3).

Answer the following parts. (i) Write down the first four terms of the sequence whose sum is represented by

S_n

. Identify its first term

a

and common difference

d

. (ii) Explain clearly how the coefficient of

k

and the constant term inside the sigma sign relate to

a

and

d

of the underlying arithmetic progression. (iii) Expand the series in ordinary addition form when

n=4

and verify that this matches your answer in part (i).