For an arithmetic progression

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

Problem

For an arithmetic progression, the sum of the first

m

terms is

p

and the sum of the first

n

terms is

q\;(m\neq n)

. (i) Derive expressions for the first term

a

and the common difference

d

in terms of

m,\,n,\,p

and

q

. (ii) Using your expressions, find

a

and

d

when

m=5,\;p=55

and

n=11,\;q=165