Geometric Mean and Properties of a GP

Three Consecutive Terms of a GP

Three numbers are in GP if they can be written as $\dfrac{a}{r},\ a,\ ar$ — writing them this way is often more convenient than $a, ar, ar^2$ because the middle term stays simply $a$.

Geometric Mean (GM) of Two Numbers

If $a$ and $b$ are two positive numbers, their Geometric Mean $G$ is the number that makes $a, G, b$ a GP. Since $\dfrac{G}{a} = \dfrac{b}{G}$, cross-multiplying gives $G^2 = ab$, so:

The Geometric Mean is used in Statistics as an average, and also whenever a single 'typical' multiplying factor is needed between two values — for example, an average growth rate between two years' figures. …