In mathematics, a pattern describes a repeated change. In the example below, matches have been placed together to create three figures.
It is possible to find a pattern? Each figure has one more triangle than the last. Therefore, the next figure should have 4 triangles.
The number of matches increases by 2, and the pattern will continue for the next figures. The first figure has 3 matches, the second 5, etc.
Using this pattern, the fourth figure should have 9 matches, the fifth 11, the sixth 13, etc. It can be described as the following arithmetic sequence:
For an arithmetic sequence, the difference between consecutive terms is constant. Meaning, the difference between the first and second term is the same as the difference between the second and the third term, and so forth. This difference is called the common difference and is usually denoted with d. An example of an arithmetic sequence is the following.
Because their terms change by a constant amount, arithmetic sequences show a linear relationship. Here, the common difference d=1.5 can be considered the slope of the line. In fact, when plotting an arithmetic sequence in a coordinate plane, it resembles the graph of a linear function.
In a theater, there are 10 rows of seats. The first row has 11 seats, and for each subsequent row, the number of seats increases by 3. Write an arithmetic sequence to represent the number of seats in each row, then graph the sequence.
Lastly, to graph the sequence, we can plot the points from the table. Notice that the points aren't connected. This is because the row number and the number of seats in each row both have to be whole numbers.