A museum intends to place benches along a straight garden path
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A museum intends to place benches along a straight garden path. The first bench will be positioned 3 m from the entrance gate, and each successive bench will be placed 2 m farther from the previous one.
Respond to the points given below:
(i) Describe in words the pattern followed by the distances of the benches from the entrance.
(ii) Explain why these distances constitute an arithmetic progression and state its common difference.
(iii) The planners wish the last bench to be no farther than 63 m from the entrance. Without performing any numerical calculations, outline the logical steps that would be taken to decide how many benches can be installed.