Start by making a chart showing the number of people that can be seated in the first three arrangements.
Rule: a_n=2+4n Graph:
Practice makes perfect
We will first write a rule for the number of people that can be seated around n tables. Then, we will use the rule to draw the graph of the sequence.
Writing a Rule
Let's make a chart showing the number of people that can be seated in the first three arrangements. Let a_n be the number of people around n tables.
Tables, n
1
2
3
Number of People, a_n
6
10
14
In the diagram, we see that there are 2 chairs on the left and right of the table, and each time 4 chairs are added. With these in mind, let's rewrite the second row of the chart.
Tables, n
1
2
3
Number of People, a_n
6=2 + 4( 1)
10=2+ 4( 2)
14=2+ 4( 3)
We have shown how the number of people and table are related. For n tables, 2+4n gives the number of people that can be seated.
a_n=2+4 n
Graphing the Sequence
To draw the graph of the sequence, we will make a table of values.
