Solve the problem.
-A brick staircase has a total of 15 steps The bottom step requires 114 bricks. Each successive step requires 5 fewer bricks than the prior one. How many bricks are required to build the staircase?
A)1185 bricks
B)2235 bricks
C)2370 bricks
D)1147.5 bricks

Question

Quizplus · Accepted Answer

The total number of bricks required for the staircase can be found using the formula for the sum of an arithmetic series, $S_n = \frac{n}{2}(a_1 + a_n)$, where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term. Here, $n = 15$, $a_1 = 114$, and $a_n = 114 - 5(15 - 1) = 114 - 70 = 44$. Plugging these values into the formula gives $S_{15} = \frac{15}{2}(114 + 44) = 7.5 \times 158 = 1185$.

Solve the Problem. -A Brick Staircase Has a Total of 15 Steps the 15