Chapter 4.6, Problem 53E

To determine

To calculate: How many logs are in the pile.

Answer to Problem 53E

Total logs in a pile are $119$ .

Explanation of Solution

Given information: 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: From given information sequence is $20,19,\mathrm{.......14}$ .

  $a=20\mathrm{and}d=19-20=-1$ .

  $\begin{array}{l}{a}_n=14\\ a+(n-1)d=14\\ 20+(n-1)(-1)=14\\ 20-n+1=14\\ 21-14=n\\ 7=n\\ s_n=\frac{n}{2}(a+a_n)\\ s_7=\frac{7}{2}(20+14)\\ s_7=\frac{7}{2}(34)=7(17)=119\end{array}$

Therefore total logs in a pile are $119$ .