# Arithmetic, Geometric & Exponential Patterns

You have actually been working with algebra since you were three and began to notice patterns (red dog, blue cat, red dog, blue cat…). The patterns we are going to work with now are just a little more complex and may take more brain power. Patterns are the beginning of algebra.

There are endless types of patterns and methods for solving patterns. You mostly have been working with simple arithmetic (patterns involving adding or subtracting a number each time) or geometric patterns (ones involving multiplying or dividing by a number).

Here are three common types of patterns you may have seen.

Type | Example | Solution |
---|---|---|

Arithmetic | 1,3,5,7,9... | Add 2 each time. |

99,90,81,72... | Subtract 9 each time | |

Geometric | 1,2,4,8,16... | Multiply the previous number by 2. |

1000,100,10,1... | Divide the previous number by 10. | |

Geometric - Exponential | 2,4,16,256... | Square the previous number. |

1,4,9,16,25... | 1^{2},2^{2},3^{2},4^{2},5^{2}... |

**Look Out**: an exponential pattern is actually a type of geometric pattern. However, to help explain things, we made them a subcategory.