Question

A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two bricks less than the previous step

How many bricks are required to build the stair case?

Answer 1

100 + 98 + 96 + 94 + … 30 steps.

Here

a = 100

d = – 2

n = 30

∴ S_n = `"n"/2`  (2a + (n – 1)d)

S₃₀ = `30/2` (2 × 100 + 29 × – 2)

= 15(200 – 58)

= 15 × 142

= 2130

No. of bricks required to build the stair case are 2130.