Definition:Arithmetic-Geometric Sequence

Definition
An arithmetic-geometric progression is a sequence $\left \langle{a_n}\right \rangle$ in $\R$ defined as:
 * $a_n = \left({a_0 + n d}\right) r^n$ for $n = 0, 1, 2, \ldots$

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

Linguistic Note
In this context, the word arithmetic is pronounced with the stress on the first and third syllables: a-rith-me-tic, rather than on the second syllable: a-rith-me-tic.

This is because the word is being used in its adjectival form.