MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Let {an} be an arithmetic progression.
(i) Prove that for any positive integers p,q,r,s satisfying p+q=r+s, we have ap+aq=ar+as.
(ii) In an arithmetic progression of 25 terms, the 3rd term is 8 and the 14th term is 47. Using the result of part (i), find the sum of the 6th and 11th terms.
(iii) Hence determine the common difference of the progression described in part (ii).