# Sequence An **[[Arithmetic Sequence]]** is a sequence in which the **difference between two adjacent terms is constant**. A **[[Geometric Sequence]]** is one in which **the ratio between two adjacent terms is constant**. An [[Arithmetic-Geometric Sequence]] is a combination of the two previous sequences. The [[Fibonacci Sequence]] is a popular sequence which is usually defined recursively as the sum of the previous two terms. **The sum of elements in a sequence is called a [[Series]]**. If the number of elements is infinite, you're dealing with an [[Infinite Series]]. Number sequences **can be defined in several ways** (all example define the same sequence): - ***By property***, when the terms of the sequence all share a particular property. The sequence is then **ordered using a particular method. For example, odd numbers**. - ***Recursively***, when the next term is a function of the previous one i.e. through [[Recursion]]. For example, $a_1=1, a_n=a_{n-1}+2$. This method is usually the simplest one to determine, by looking for patterns between two adjacent terms. - ***Explicitly*, when a formula is provided for the n-th term**. For example, $a_n = 2n-1$. The benefit of this method is that you can easily calculate n-th term without calculating any of the previous ones.