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Section 17.1 Defining a Sequence
The shortest way to list the terms in a sequence is using the $ symbol in Maple. As an example, we may wish to list the elements of the sequence
\begin{equation*}
\displaystyle\left\lbrace3k^2+2\right\rbrace_{k=0}^3\text{.}
\end{equation*}
This should give four integers that follow the form of \(3k^2+2\) from index \(k=0\) up to \(k=3\text{.}\)
A dollar symbol is used after the expression of a generic term of the sequence, followed by specifying an interval for the index.
\begin{equation*}
\displaystyle 2,\,5,\,14,\,29
\end{equation*}
The index does not have to start at zero. Here are five integers of the sequence
\(\left\lbrace2k^2-k\right\rbrace_{k=1}^5\text{:}\)
\begin{equation*}
\displaystyle 1,\,6,\,15,\,28,\,45
\end{equation*}
We can also list the terms in a sequence by using the
seq() command. This command essentially performs the same operation as the $ symbol. Here is that same sequence again, using the
seq() command.
\begin{equation*}
\displaystyle 1,\,6,\,15,\,28,\,45
\end{equation*}
