# Category:Geometric Progressions

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This category contains results about Geometric Progressions.

Definitions specific to this category can be found in Definitions/Geometric Progressions.

A **geometric progression** is a sequence $\left \langle{x_n}\right \rangle$ 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:

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

## Also see

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### G

### S

## Pages in category "Geometric Progressions"

The following 14 pages are in this category, out of 14 total.

### E

- Elements of Geometric Progression from One Divisible by Prime
- Elements of Geometric Progression from One where First Element is not Power of Number
- Elements of Geometric Progression from One where First Element is Power of Number
- Elements of Geometric Progression from One which Divide Later Elements