Question

A brick staircase has a total of 17 steps The bottom step requires 131 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?

Answer 1

Answer: 1547 bricks are required to build the staircase.

Step-by-step explanation:

We are given:

Number of bricks in the first step, $a_1$ = 131

Number of bricks in the second step, $a_2$ = 131 - 5 = 126

Number of bricks in the third step, $a_3$ = 126 - 5 = 121

Sequence become:

131, 126, 121, .....

These are in arithmetic progression where a = 131 and d (common difference) = -5

To calculate the sum of an AP, we use the formula:

$S_n=\frac{n}{2}[2a+(n-1)d]$

where,

n = number of terms = 17

Putting values in above equation, we get:

$S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547$

Hence, 1547 bricks are required to build the staircase.