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kayden1234thomp
25.07.2019 •
Mathematics
Constructing a brick staircase: a brick staircase has a total of 30 steps. the bottom step requires 100 bricks. each successive step requires two less bricks than the prior step a) how many bricks are required for the top shelf? b) how many bricks are required to build the staircase sequences, pre-calc show all work : )
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Ответ:
a_n = 100 - 2(n-1) = 102 - 2n, and for the 30th step, a_30 = 102 - 2*30 = 42. So the top step will need 42 bricks.
b) The total staircase will need: 100 + 98 + 96 + ... + 44 + 42, and there are n = 30 terms. Using the formula for the sum of an arithmetic sequence:
S = (a_1 + a_n)*n/2 = (100 + 42)*30/2 = 2130
Therefore, 2130 bricks are required to build the entire staircase.
Ответ:
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