A carpenter makes a ladder whose rungs have lengths (in cm): 60, 57.5, 55, 52.5, …
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A carpenter makes a ladder whose rungs have lengths (in cm): 60, 57.5, 55, 52.5, …
(i) Prove that the lengths of the rungs form an arithmetic progression and find its common difference.
(ii) If the shortest rung must not be shorter than 32.5 cm, determine the maximum number of rungs the carpenter can use.
(iii) For the number of rungs found in part (ii), calculate the total length of all the rungs combined.