MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
For a certain arithmetic progression, the sum of the first 2n terms is three times the sum of its first n terms.
(i) Show that 2a=(n+1)d, where a is the first term and d is the common difference.
(ii) If n=5 and the 5th term is 21, find the values of a and d.
(iii) Using the values obtained in (ii), determine the sum of the first 15 terms of the progression.