In an arithmetic progression (A.P.) the sum of the first 20 terms is 220 while the…

MATHEMATICS · Multi-part · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

In an arithmetic progression (A.P.) the sum of the first 20 terms is 220 while the sum of the first 30 terms is 510. (i) Find the first term

a

and the common difference

d

of the A.P. (ii) Hence determine the

25^{\text{th}}

term of the progression.