Geometric Mean of Terms of a GP

Geometric Mean of Terms of a GP

## Formula

For positive terms of a GP:

$$a,ar,ar^2,\ldots,ar^{n-1}$$

the geometric mean is:

$$\sqrt[n]{a\cdot ar\cdot ar^2\cdots ar^{n-1}}$$

Therefore:

$$GM=ar^{(n-1)/2}$$

## Conditions / Special Cases

This formula applies directly when the terms are positive.

For an odd number of terms, the geometric mean equals the middle term.

## Usage

- Used to find the geometric mean of all terms in a GP.