Definition:Arithmetic-Geometric Sequence

Definition
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:
 * $a_0, \paren {a_0 + d} r, \paren {a_0 + 2 d} r^2, \paren {a_0 + 3 d} r^3, \ldots$

Also known as
An arithmetic-geometric sequence is also (more usually) known as an arithmetic-geometric progression.

prefers the word sequence because it is less ambiguous than progression, which is sometimes also seen to mean series.