Consider an arithmetic progression whose 8th term exceeds its 3rd term by 25 and…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Consider an arithmetic progression whose 8th term exceeds its 3rd term by 25 and whose 13th term exceeds its 10th term by 7.
(i) Express the 8th and 3rd terms in terms of the first term a and the common difference d, and hence obtain an equation relating a and d.
(ii) Express the 13th and 10th terms in terms of a and d, and obtain a second equation relating a and d.
(iii) Explain whether the two equations obtained in parts (i) and (ii) are sufficient to determine unique values of a and d. Give a reason for your answer.