# Category:Geometric Sequences

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This category contains results about **Geometric Sequences**.

Definitions specific to this category can be found in **Definitions/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

## Subcategories

This category has the following 4 subcategories, out of 4 total.

### G

- Geometric Series (empty)

### S

- Sum of Powers of 2 (3 P)

## Pages in category "Geometric Sequences"

The following 16 pages are in this category, out of 16 total.