, a mixture of the two which always lies in between. The geometric mean is also the arithmetic-harmonic mean in the sense that if two sequence s ( a n ) and ( h n ) are defined: a_{n+1} = \frac{a_n + h_n}{2}, \quad a_0=x and h_{n+1} = \frac{2}{\frac{1}{a_n} + \frac{1}{h_n}},