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# 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: 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. |

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