Key Equations

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 [latex]n\text{th}[/latex] 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 [latex]n[/latex] is the product of all integers from 1 to [latex]n[/latex]

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 [latex]\left\{1,2,\dots n\right\}[/latex] for some positive integer [latex]n[/latex]

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

n factorial the product of all the positive integers from 1 to [latex]n[/latex]

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

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