In an arithmetic progression the -th term is and the -th term is

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

and

q

are distinct positive integers. (i) Show that the

(p + q)

-th term of the progression is

0

. (ii) Hence obtain expressions for the first term and the common difference in terms of

p

and

q

. (iii) Using the result of part (ii), determine the first term and the common difference when

p = 4

and

q = 7