\begin{frame}
\frametitle{Defining sequences}
\begin{question}
How can we define a sequence of numbers $\left(a_1, a_2, a_3 \dots, a_n, \dots \right)$?
\end{question}
\begin{itemize}
\item<2-> A sequence can be interpreted as a function that takes as arguments a subset of the integers. 
\item<3-> Since functions can be defined in exotic and indirect ways, so can sequences. 
\item<4-> We will focus on the three most frequently used ways to define sequences:
\begin{itemize}
\item<5-> by specifying a formula for the $n^{th}$ term;
\item<6-> by recursion;
\item<7-> by specifying a property of integers and constructing a sequence of all integers with that property.
\end{itemize}
\end{itemize}
\end{frame}