Many sequences do not follow the pattern of geometric or arithmetic. These sequences have their own patterns. Some can be modeled by other polynomial functions.

Example 1 The following sequence models triangular numbers:

1, 3, 6, 10, 15, 21, 28, 36, 45 …

This sequence is generated from a pattern of dots that form a triangle.
By adding another row of dots and counting all the dots, we can find the next number of the sequence.


The symbolic pattern for this sequence is to add 2 to the first term, add 3 to the second term, add 4 to the fourth term and so on. This type of sequence has a constant second difference and can be modeled by the quadratic function OtherEx1-2.