\begin{definition}[Definition:Arithmetic-Geometric Sequence]
An '''arithmetic-geometric sequence''' is a sequence $\sequence {a_k}$ in $\R$ defined as:
:$a_k = \paren {a_0 + k d} r^k$
for $k = 0, 1, 2, \ldots$
Thus its general form is:
:$a_0, \paren {a_0 + d} r, \paren {a_0 + 2 d} r^2, \paren {a_0 + 3 d} r^3, \ldots$
\end{definition}