Mathematics

Problem

In an arithmetic progression it is known that the

p

-th term is

q

and the

q

-th term is

p

, where

p \neq q

. a. (i) Using the information above, write two equations in the first term

a

and common difference

d

. b. (ii) Solve these equations to express

a

and

d

in terms of

p

and

q

. c. (iii) Hence or otherwise, prove that the

(p+q)

-th term of the progression is zero.