© 2016 Shmoop University, Inc. All rights reserved.
Basic Algebra

Basic Algebra

Arithmetic, Geometric & Exponential Patterns Examples

Example 1

The first four triangle numbers are 1, 3, 6, and 10. They are called triangular because they can be arranged in dots as triangle, like so:

triangles (example #1)

What will the 10th triangular number be?

Example 2

Find the next two numbers in this pattern: 1, 2, 8, 48, 348…

Some of you may have figured out the pattern by just looking at it, the rest of us may need a little help. Let's start by writing these numbers in a chart and looking at their differences.

pattern 2

Example 3

Find the missing number in the pattern: 3, 9, 81, ___, 43046721.

As mentioned before, there are three basic types of patterns: arithmetic, geometric, and geometric exponential. Let's try all three and see if one fits.

pattern 5

Here you can see that geometric-exponential patterns are also geometric. We can use either of these patterns to fill in the blanks.