MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Some geometric means are inserted between 5 and 320. The sum of all the inserted means is 310.
(i) If q geometric means are inserted and the common ratio is r, express the sum of the q means in terms of q, r and the first term.
(ii) Form an equation in q by using the facts that the last term is 320 and the sum of the inserted means is 310.
(iii) Hence determine the number of geometric means inserted and write them explicitly.