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Geometric Sequence


A geometric sequence, also called a geometric progression or geometrical progression, is a sequence {a_k}, k=0, 1, ..., in which each term after the first is the preceding term multiplied by a fixed multiplier r. For a sequence whose terms are all nonzero, an equivalent definition is that it is geometric iff it has zero series bias. If the multiplier is r, then for k>=2 the kth term is given by

 a_k=ra_(k-1)=r^2a_(k-2)=a_0r^k.
(1)

Taking a_0=1 gives the simple special case

 a_k={1   for k=0; r^k   for k>=1.
(2)

The Season 1 episode "Identity Crisis" (2005) of the television crime drama NUMB3RS mentions geometric progressions.


See also

Arithmetic Progression, Common Ratio, Erdos Similarity Conjecture, Geometric Series

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Cite this as:

Weisstein, Eric W. "Geometric Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeometricSequence.html

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