Relation Between Equidistant Terms of a GP

Relation Between Equidistant Terms of a GP

## Formula

For a GP with $$n$$ terms:

$$a_r\cdot a_{n-r+1}=a_1a_n$$

More generally:

$$a_{r-k}\cdot a_{r+k}=a_r^2$$

## Conditions / Special Cases

Three consecutive terms of a GP satisfy:

$$b^2=ac$$

if the terms are:

$$a,b,c$$

## Usage

- Used to establish relationships between terms without finding the common ratio.