Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-A brick staircase has a total of 18 steps The bottom step requires 101 bricks. Each successive step requires 4 fewer bricks than the prior one. How many bricks are required to build the staircase?
A) 1206 bricks
B) 2430 bricks
C) 2412 bricks
D) 1170 bricks

Question

Quizplus · Accepted Answer

The sum of the first n terms of an arithmetic sequence is given by the formula $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first n terms, $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the nth term. Here, $n = 18$, $a_1 = 101$, and since each step requires 4 fewer bricks than the previous one, the common difference $d = -4$. The 18th term $a_{18} = a_1 + (n-1)d = 101 + (18-1)(-4) = 101 - 68 = 33$. Thus, the total number of bricks required is $S_{18} = \frac{18}{2}(101 + 33) = 9 \times 134 = 1206$ bricks.

Use the Formula for the Sum of the First N