Definition:Arithmetic-Geometric Sequence

Definition
An arithmetic-geometric progression is a sequence $\left \langle{a_k}\right \rangle$ in $\R$ defined as:
 * $a_k = \left({a_0 + k d}\right) r^k$

for $k = 0, 1, 2, \ldots$

Thus its general form is:
 * $a_0, \left({a_0 + d}\right) r, \left({a_0 + 2 d}\right) r^2, \left({a_0 + 3 d}\right) r^3, \ldots$