For an arithmetic progression whose first term is and common difference is

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

Problem

For an arithmetic progression whose first term is

a

and common difference is

d

, the sum of the terms from the

(n+1)

th term to the

(2n)

th term equals 5 times the first term and is also equal to 180. (i) Obtain an expression, in terms of

a

d

and

n

, for the sum of the terms from the

(n+1)

th term to the

(2n)

th term. (ii) Hence form two equations involving

a

d

and

n

. (iii) If the common difference

d

is a positive integer less than 10, determine the values of

a

d

and

n