A brick staircase has a total of 30 steps The bottom step re

A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two less bricks than the prior step. (a) How many bricks are required for the top step? (b) How many bricks are required to build the staircase?

Solution

total steps = 30

bottom requires 100 bricks

a1 = 100

d = - 2

an = a1 + (n-1)d

a30 = 100 + ( 30-1) -2

a30 = 100 - 58

a30 = 42

so top step requires 42 bricks

b) applying sum of arithmetic series formula

Sn = n/2 ( a1 + an )

Sn = 30/2 ( 100 + 42 )

Sn = 2130

total bricks required is 2130