Chapter 12, Problem 34RE

a.

To determine

To find:Number of bricks required for top step.

Answer to Problem 34RE

The number of bricks required for top step is 8.

Explanation of Solution

Given:

A brick staircase has 25 steps and bottom step requires 80 bricks.

Calculation:

By arithmetic progression,

  $a_n=a+\left(n-1\right)d$

Here,

  $a=80d=-3$

Therefore,

  $\begin{array}{l}\Rightarrow a_{25}=80+\left(25-1\right)\left(-3\right)\\ \Rightarrow a_{25}=80+\left(24\right)\left(-3\right)\\ \Rightarrow a_{25}=80-72\\ \Rightarrow a_{25}=8\end{array}$

Hence,the number of bricks required for top step is 8.

b.

To determine

To find:Number of bricks required to build the staircase.

Answer to Problem 34RE

Number of bricks required to build the staircase is 1100.

Explanation of Solution

Given:

A brick staircase has 25 steps and bottom step requires 80 bricks.

Calculation:

Total bricks required,

  $\begin{array}{l}=\frac{n}{2}\left(a+l\right)\\ =\frac{25}{2}\left(80+8\right)\\ =1100\end{array}$

Hence, the number of bricks required to build the staircase is 1100.