## Key Equations

 Formula for a factorial \begin{align}0!&=1\\ 1!&=1\\ n!&=n\left(n - 1\right)\left(n - 2\right)\cdots \left(2\right)\left(1\right)\text{, for }n\ge 2\end{align}

## Key Concepts

• A sequence is a list of numbers, called terms, written in a specific order.
• Explicit formulas define each term of a sequence using the position of the term.
• An explicit formula for the $n\text{th}$ term of a sequence can be written by analyzing the pattern of several terms.
• Recursive formulas define each term of a sequence using previous terms.
• Recursive formulas must state the initial term, or terms, of a sequence.
• A set of terms can be written by using a recursive formula.
• A factorial is a mathematical operation that can be defined recursively.
• The factorial of $n$ is the product of all integers from 1 to $n$

## Glossary

explicit formula a formula that defines each term of a sequence in terms of its position in the sequence

finite sequence a function whose domain consists of a finite subset of the positive integers $\left\{1,2,\dots n\right\}$ for some positive integer $n$

infinite sequence a function whose domain is the set of positive integers

n factorial the product of all the positive integers from 1 to $n$

nth term of a sequence a formula for the general term of a sequence

recursive formula a formula that defines each term of a sequence using previous term(s)

sequence a function whose domain is a subset of the positive integers

term a number in a sequence