A brick staircase has a total of 30 steps. The bottom step requires 10

1.	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?
Answer» 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 x 100 + 29 x -2) = 15(200 – 58) = 15 x 142 = 2130 t₃₀ = a + (n – 1)d = 100 + 29 x -2 = 100 – 58 = 42 (i) No. of bricks required for the top step are 42. (ii) No. of bricks required to build the stair case are 2130.

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?

Answer»

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 x 100 + 29 x -2)

= 15(200 – 58)

= 15 x 142

= 2130

t₃₀ = a + (n – 1)d

= 100 + 29 x -2

= 100 – 58

= 42

(i) No. of bricks required for the top step are 42.

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