Pattern Building: Examples

Pattern Building

Examples

Example 1 Find the pattern in the following sequence of numbers:

1, 4, 7, 10, 13, 16, 19 â€¦

The sequence goes from one term to the next by adding 3 each time. Therefore, it is arithmetic and can be modeled by a linear function. The method for finding the function will be presented later in this unit.

Example 2 Find the pattern in the following sequence of numbers:

2, 6, 18, 54, 162 â€¦

The sequence goes from one term to the next by multiplying by 3 each time. Therefore, the sequence is geometric and can be modeled by an exponential function. The method for finding the function will be presented later in this unit.

Example 3 Find the pattern in the following sequence of numbers:

-1, 4, 11, 20, 31, 44 â€¦

In this sequence, there is no constant difference or ratio. To change from term 1 to term 2, add 5. To change from term 2 to term 3, add 7. To change from term 3 to term 4, add 9. This pattern will continue from term to term and has a common second difference.

Therefore, the sequence is not arithmetic or geometric and can be modeled by a quadratic function. The method for finding the function will be presented later in this unit.