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.
(1) How many bricks are required for the top most step
(11) How many bricks are required to build the stair case?​

Answer 1

Answer:

i) 42 bricks

ii) 2130 bricks

Step-by-step explanation:

First stair needs 100 bricks, second needs two less than the first, and so on......

So, it is an AP

100, 98 , 96 ,........

a = first term = 100

d = t2 - t1 = 98 - 100 = - 2

i) To find: a30 = ?

an = a + (n-1)d

a30 = 100 + 29(- 2)

= 100 - 58

a30 = 42 bricks

ii) To find: S30 = ?

Sn = n/2[2a + (n-1)d]

S30 = 30/2( 200 - 58)

= 15(142)

S30 = 2130 bricks

Hope it helps you:)