Arithmetic Sequences
Problem Solution
One approach to solving the problem is to make a table in order to see if there is a pattern that relates the number of tables to the number of people that can be seated.
| Number of Tables | Diagram | Number of Seats |
|---|---|---|
| 1 |  |
4 |
| 2 |  |
6 |
| 3 |  |
8 |
| 4 |  |
10 |
The pattern that is emerging is clearly an arithmetic sequence. The numbers in the sequence begin 4, 6, 8, 10, ... .
To find the number of people that can sit at 20 tables, use the formula:
The nth term of an arithmetic sequence = a + [(n - 1) X d]
The first element = a = 4. The common difference = d = 2.
The term = n = 20.The 20th term = 4 + [(20 - 1) X 2] = 4 + [19 X 2] = 4 + 38 = 42
Therefore, 42 people could sit at 20 tables.
To find the number of people that can sit at 1000 tables, use the formula.
The first element = a = 4. The common difference = d = 2. The term = n = 1000.
The 1000th term = 4 + [(1000 - 1) X 2] = 4 + [999 X 2] = 4 + 1098 = 2002
Therefore, 2002 people could sit at 1000 tables.
email the author: Bruce Jacobs
Last modified: Thursday, February 6, 2003