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.

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.
(i) How many bricks are required for the top most step?
(ii) How many bricks are required to build the stair case?
Solution :
Let "l" be the number of bricks in the last step
Number of bricks in the 1st step (a)  = 100
Number of bricks in the 2nd step  = 100 - 2 = 98
d  = 98 - 100  = -2
number of steps (n)  = 30
(i)
t30  = a + 29d
  =  100 + 29(-2)
  =  100 - 58
  =  42
Hence in the top most step, we will have 42 bricks.
(ii) How many bricks are required to build the stair case?
Sn  = (n/2)[a + l]
  =  (30/2)[100 + 42]
  =  15(142) 
  =  2130

No comments: