An arithmetic progression is such that the ratio of the sum of its first 25 terms to…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
An arithmetic progression is such that the ratio of the sum of its first 25 terms to the sum of its first 15 terms is 7 : 3. The 10th term of the progression is 29.
Answer the following questions based on this information.
(i) Frame an equation in the first term a and common difference d using the given ratio of the two sums.
(ii) Form a second equation in a and d using the information about the 10th term, and hence determine the values of a and d.
(iii) Using the values of a and d obtained in part (ii), find the 40th term of the progression.