In an arithmetic progression

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

Problem

In an arithmetic progression, the

p

th term is

q

and the

q

th term is

p

, where

p \ne q

. (a) Form two equations in the first term

a

and the common difference

d

using the given information, and hence obtain the value of

d

. (b) Using the value of

d

, find the first term

a

in terms of

p

and

q

. (c) Show that the

(p+q)

th term of the progression is 0.