Chapter 8.1, Problem 29E

To determine

To Find: A rule for the number of people that can be seated around the $n$ tables arranged in this manner. Then graph the sequence.

Answer to Problem 29E

  $a_n=4n+2$

Explanation of Solution

Given: Rectangular tables are placed together along their short edges, as shown in the diagram.

  

Notice that the pattern form from the figure is

  $\begin{array}{l}{a}_1=4\times 1+2=6\\ a_2=4\times 2+2=10\\ a_3=4\times 3+2=14\end{array}$

Thus

The $nth$ term of the sequence is

  $a_n=4n+2$

The graph of the sequence is shown below.