The sum of the first eight terms of an arithmetic progression is 136

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

Problem

The sum of the first eight terms of an arithmetic progression is 136, while the sum of the first twenty terms is 820. (i) Let the first term be

a

and the common difference be

d

. Form two equations in

a

and

d

from the information given. (ii) Solve these equations to obtain the values of

a

and

d

. (iii) On the basis of the value of

d

found, state whether the progression is increasing or decreasing. Justify your answer.