A staircase is designed so that the length of each successive step forms an…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A staircase is designed so that the length of each successive step forms an arithmetic progression. The 3rd step is 44 cm long and the 15th step is 86 cm long. The staircase has 25 steps in total.
(i) Determine the common increase in length between consecutive steps.
(ii) Find the length of the first step.
(iii) Calculate the combined length of all 25 steps.
(iv) Safety regulations stipulate that no step should exceed 100 cm in length. Verify whether this staircase satisfies the regulation.