Chapter SH, Problem 10.7EP

To determine

To find: The number of cup required to stack the cups up to 8 rows.

Answer to Problem 10.7EP

Total 36 cups are required to stack the cups 8 rows high.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

From the given figure the arithmetic series is 1, 2, 3, 4,….

Find the common difference.

  $\begin{array}{c}2-1=1\\ 3-2=1\\ 4-3=1\\ ⋮\end{array}$

Find the sum of the arithmetic series.

  $\begin{array}{c}{S}_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]\\ S_8=\frac{8}{2}\left[2\left(1\right)+\left(8-1\right)1\right]\\ =4\left(2+7\right)\\ =36\end{array}$

Therefore, total 36 cups are required to stack the cups 8 rows high.