geometric sequence

A sequenceMathworldPlanetmathPlanetmath of the form


of real or complex numbers is called geometric sequenceMathworldPlanetmath.  of the geometric sequence is thus that every two consecutive members of the sequence have the constant ratio r, called usually the common ratio of the sequence (if  ar=0, speaking the ratio of members does not exist).

The nth member of the geometric sequence has the


Let  a0.  The sequence is convergentMathworldPlanetmathPlanetmath for  |r|<1  having the limit ( 0, and for  r=1  having as constant sequence the limit a.

When the members of the sequence are positive numbers, each member is the geometric mean of the preceding and the following member; the name “geometric sequence”(or “geometric seriesMathworldPlanetmath”) is due to this fact (a fact is true for the harmonic series and harmonic mean).

Title geometric sequence
Canonical name GeometricSequence
Date of creation 2013-03-22 14:38:52
Last modified on 2013-03-22 14:38:52
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 14
Author pahio (2872)
Entry type Definition
Classification msc 40-00
Related topic GeometricSeries
Related topic LimitOfRealNumberSequence
Defines common ratio