Definition:Arithmetic-Geometric Progression

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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:

$a_0, \left({a_0 + d}\right) r, \left({a_0 + 2 d}\right) r^2, \left({a_0 + 3 d}\right) r^3, \ldots$

Also see

  • Results about Arithmetic-Geometric Progressions can be found here.

Linguistic Note

In the context of an arithmetic progression or arithmetic-geometric progression, 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.