A brick staircase has a total of 40 steps The bottom step re

A brick staircase has a total of 40 steps. The bottom step requires 88 bricks. Each successive step requires two less bricks than the prior step. How many bricks are required for the top step? How many bricks are required to build the staircase?

Solution

Bricks in steps can be written as a series : 88, 86 , 84 , 82 , 80 -----

Its an A.P series common diffetence , d=-2 ; a1 =88

a) top step i.e. 40th:

a40 = a1 + (n-1)d

= 88 +(39*(-2)

= 10 bricks

b) Total no. of bricks = sum of series = (n/2)[a1 +a40]

= (40/2)[ 88+10]

= 1960 bricks