Chapter 4.6, Problem 53E

To determine

To find: the number of logs is in the pile.

Answer to Problem 53E

The number of logs in the pile is 119 logs.

Explanation of Solution

Given:

Consider the firewood is stacked in a pile. The bottom row has 20 logs, and the top row has 14 logs. Each row has one more log than the row above it.

Calculation:

Let us assume the number of rows is n and the difference is d .

Consider the function for $n^{th}$ term

  $f\left(n\right)=a+\left(n-1\right)d$

Put the values $a_1=14$ , $d=1$ and $f\left(n\right)=20$

  $\begin{array}{l}20=14+\left(n-1\right)\left(1\right)\\ 20=14+n-1\end{array}$

Take the variable at one side and find the value

  $n=7$

Now, find each term

  $a_2=15,a_3=16,a_4=17,a_5=18,a_6=19\text{ and }{a}_7=20$

Total logs in the pile is

  $\begin{array}{l}\text{Total logs }=a_1+a_2+a_3+a_4+a_5+a_6+a_7\hfill \\ \begin{array}{l}=14+15+16+17+18+19+20\\ =119\end{array}\hfill \end{array}$

Conclusion:

Therefore, the number of logs in the pile is 119 logs.