Question

Which one of the following is true about $AM,GM$ and $HM.$

• A. $H.M.\ge G.M\ge A.M$
• B. $A.M.\ge H.M\ge G.M$
• C. $A.M.\ge G.M\ge H.M$
• D. $G.M.\ge H.M\ge A.M$

Answer 1

The correct option is C $A.M.\ge G.M\ge H.M$

Let $a_1,a_2,a_3........a_n$ be $n$ positive real number then we define their
$A.M=\frac{a_1,a_2,a_3.........a_n}{n}$ their
$G.M=(a_1,a_2,a_3.......a_n{)}^{\frac{1}{n}}$and their
$H.M=\frac{n}{\frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}+........+\frac{1}{a_n}}$
Then it can be shown $A.M.\ge G.M\ge H.M$