(A) For any two distinct positive real numbers $a$ and $b$,the arithmetic mean $A = \frac{a+b}{2}$,geometric mean $G = \sqrt{ab}$,and harmonic mean $H

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(A) For any two distinct positive real numbers $a$ and $b$,the arithmetic mean $A = \frac{a+b}{2}$,geometric mean $G = \sqrt{ab}$,and harmonic mean $H = \frac{2ab}{a+b}$.We know that $A \times H = \left(\frac{a+b}{2}\right) \times \left(\frac{2ab}{a+b}\right) = ab = G^2$.Thus,$G^2 = AH$,which implies $G$ is the geometric mean of $A$ and $H$.For distinct positive real numbers,$A > G > H$ always holds true.

Class 11 Mathematics Sequences and Series Relation between A.P., G.P.

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If the arithmetic,geometric,and harmonic means between two distinct positive real numbers are $A, G,$ and $H$ respectively,then the relation between them is

A
$A > G > H$
B
$A > G < H$
C
$H > G > A$
D
$G > A > H$

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Relation between A.P., G.P.

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If the arithmetic,geometric,and harmonic means between two distinct positive real numbers are $A, G,$ and $H$ respectively,then the relation between them is

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