An architect designs a staircase for a hotel lobby such that the first step has a…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
An architect designs a staircase for a hotel lobby such that the first step has a rise of 17 cm. For aesthetic reasons, the rise of each subsequent step is reduced uniformly by 0.3 cm compared with the previous step. The lobby floor is exactly 2.89 m above the ground floor.
Using this information, answer the following:
(i) Determine the number of steps required to reach the lobby floor.
(ii) Calculate the rise of the last step.
(iii) Find the total vertical distance climbed after the first 15 steps and state whether this is sufficient to reach the lobby floor.