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%TCIDATA{<META NAME="Title" CONTENT="Reference/Mathematics/Sequences">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
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\section{Sequences\label{Sequences}}

A \emph{sequence} is a set of numbers written in a specific order: 
\[
a_{1}a_{2}a_{3}a_{4}...,a_{n},...
\]
The number $a_{1}$ is called the \emph{first term}; $a_{2}$ is the \emph{%
second term}, and in general $a_{n}$ is the $n$\emph{th term}. Since for
every natural number $n$ there is a corresponding number $a_{n}$, we can
define a sequence as a function.

\subsection{Definition of a Sequence\label{Definition of a sequence}}

A \textbf{sequence} is a function $f$ whose domain is the set of natural
numbers. The values $f(1),f(2),f(3),...$ are called the \textbf{term}s of
the sequence.

The $n$th term of a sequence may depend on some or all of the terms
preceding it; such a sequence is called \textbf{recursive}.

\subsection{\ Related Reference Topics\hfill}

{\small \hyperref{Sequence}{}{}{Cal09_01.tex#sequences}}

\subsection{Related Scientific Notebook Topics}

{\small \hyperref{Plotting sequences}{}{}{../../Help/DM7-7.tex#Plotting
sequences}}

{\small \hyperref{Sequences in Scientific Notebook}{}{}{%
../../Help/DM7-7.tex#Sequences}}

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