Consider an arithmetic progression with first term and common difference .

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

Problem

Consider an arithmetic progression with first term

a

and common difference

d

. (i) Explain why the sum of the terms from the

p

-th to the

q

-th term (inclusive), where

q>p\ge 1

, can be written as

S_q-S_{p-1}

, where

S_n

denotes the sum of the first

n

terms of the progression. (ii) Using the result of part (i), obtain a simplified expression, in terms of

a

d

p

and

q

, for the sum

T_{p,q}=a_p+a_{p+1}+\dots +a_q