Question

Find the AM, GM and HM between $9$ and $18$

Answer 1

We know that the arithmetic mean between the two numbers $a$ and $b$ is $AM=\frac{a+b}{2}$, the geometric mean is $GM=\sqrt{ab}$ and the harmonic mean is $HM=\frac{2ab}{a+b}$.

Here, it is given that $a=9$ and $b=18$, therefore,

$AM=\frac{a+b}{2}=\frac{9+18}{2}=\frac{27}{2}$

$GM=\sqrt{ab}=\sqrt{9\times 18}=\sqrt{162}=9\sqrt{2}$

$HM=\frac{2ab}{a+b}=\frac{2\times 9\times 18}{9+18}=\frac{324}{27}=12$

Hence, $AM=\frac{27}{2}$, $GM=9\sqrt{2}$ and $HM=12$