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?
a
f
AD 1
Answers
Answer:
[i]42
[ii]2130
Step-by-step explanation:
a=100
n=30
d=-2
t30=?
s30=?
1] tn=a+[n-1]d
t30=100+29[-2]
t30=100-58
t30=42
2]sn=n/2[2a+[n-1]d]
S30=30/2[200+-[58]]
=15*142
=2130
42 Bricks required for top most step and 2130 bricks required to build the stair case
Step-by-step explanation:
100 bricks required for Bottom step
Total Step = 30
each successive step needs 2 brick less than the previous step
This is an AP
a = 100
d = - 2
n = 30
bricks are required for the top most step that means 30th step
= a + (30-1)d
= 100 + 29(-2)
= 100 - 58
= 42
42 Bricks required for top most step
bricks required to build the stair case
= (n/2)(a + L)
= (30/2)(100 + 42)
= 15 * 142
= 2130 Bricks
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