Solve the problem.
-A brick staircase has a total of 16 steps The bottom step requires 117 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?
A) 1232 bricks
B) 1272 bricks
C) 2544 bricks
D) 2472 bricks

Question

Quizplus · Accepted Answer

The number of bricks required for each step forms an arithmetic sequence where the first term (a1) is 117 and the common difference (d) is -5. The number of bricks for the nth step is given by the formula: a_n = a1 + (n-1)d. The total number of bricks is the sum of the sequence: S_n = n/2 * (a1 + a_n). For 16 steps, a_16 = 117 + 15*(-5) = 42. The sum is S_16 = 16/2 * (117 + 42) = 1272 bricks.

Solve the Problem. -A Brick Staircase Has a Total of 16 Steps the 16