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Geometric progressions

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-terms geometric progressions are sequences of the form (with for an infinity of terms)

where and are constants; therefore and For example, {11, 44, 176, 704, 2816, 11264, 45056, ...} (A002089) is a geometric progression with and . In terms of growth of sequences, nonconstant arithmetic progressions have exponential growth.

Equivalently, a sequence is a geometric progression when each term is the geometric mean of the neighboring terms, i.e.

Recurrence

Generating functions

Geometric progressions have rational [ordinary] generating functions of the form

See also