Geometric mean (G.M.)

If $x$ and $y$ are two numbers of the same sign (both positive or both negative), their Geometric Mean is $G=\sqrt{xy}$. This is the value that makes $x, G, y$ a G.P., since $\dfrac Gx=\dfrac yG \Rightarrow G^2=xy \Rightarrow G=\sqrt{xy}$. …