(i) Define an arithmetic progression (AP) and write the general expression for its…

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

(i) Define an arithmetic progression (AP) and write the general expression for its

k^{\text{th}}

term. (ii) Prove that the sum

S_n

of the first

n

terms of an AP whose first term is

a

and common difference is

d

is given by

S_n=\frac{n}{2}\,[2a+(n-1)d].

(iii) Using the result obtained in part (ii), find the sum of the first eight terms of the AP

5,8,11,\dots

and hence verify the formula for this specific case.