A staircase is constructed so that the -th step from the bottom requires exactly bricks.

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

A staircase is constructed so that the

k

-th step from the bottom requires exactly

(5k+3)

bricks. (i) Derive a formula, in terms of

n

, for the total number of bricks needed to build the first

n

steps. (ii) Using the formula from (i), calculate the total number of bricks required for the first

20

steps. (iii) If

2200

bricks are available, determine the greatest number of complete steps that can be built.