Category:Definitions/Geometric Sequences

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This category contains definitions related to Geometric Sequences.
Related results can be found in Category:Geometric Sequences.

A geometric sequence is a sequence $\sequence {x_n}$ in $\R$ defined as:

$x_n = a r^n$ for $n = 0, 1, 2, 3, \ldots$

Thus its general form is:

$a, ar, ar^2, ar^3, \ldots$

and the general term can be defined recursively as:

$x_n = \begin{cases} a & : n = 0 \\ r x_{n-1} & : n > 0 \\ \end{cases}$

Also see