A brick staircase has a total of 19 steps The bottom step re

A brick staircase has a total of 19 steps The bottom step requires 146 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase? Show all work please

Solution

total steps = 19

bottom requires = 146 bricks

each successive step requires 5 less than the prior

a1 = 146

d = -5

an = a1 + ( n-1 ) d

an = 146 + 18*(-5) = 56

sum of arithmetic sequence is

S = n/2 { 146 + 56 } = 1919

therefore, total 1919 bricks are required