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Study Guides > College Algebra CoRequisite Course

Summary: Sequences and Their Notations

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 nthn\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 nn is the product of all integers from 1 to nn

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 {1,2,…n}\left\{1,2,\dots n\right\} for some positive integer nn infinite sequence a function whose domain is the set of positive integers n factorial the product of all the positive integers from 1 to nn 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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