(B) We know the fundamental inequality for any two positive numbers: $A.M. > G.M. > H.M.$Given values are $\frac{144}{15} = 9.6$,$15$,and $12$.Compari

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(B) We know the fundamental inequality for any two positive numbers: $A.M. > G.M. > H.M.$Given values are $\frac{144}{15} = 9.6$,$15$,and $12$.Comparing these values,we have $15 > 12 > 9.6$.Therefore,$A.M. = 15$,$G.M. = 12$,and $H.M. = \frac{144}{15}$.The question asks for the values in the order $H.M., G.M., A.M.$Thus,the required order is $\frac{144}{15}, 12, 15$.

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

Medium

The $A.M., H.M.$ and $G.M.$ between two numbers are $\frac{144}{15}$,$15$ and $12$,but not necessarily in this order. Then $H.M., G.M.$ and $A.M.$ respectively are

A
$15, 12, \frac{144}{15}$
B
$\frac{144}{15}, 12, 15$
C
$12, 15, \frac{144}{15}$
D
$\frac{144}{15}, 15, 12$

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Sequences and Series

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Relation between A.P., G.P.

The common difference of an $A.P.$ whose first term is unity and whose second,tenth and thirty-fourth terms are in $G.P.$ is

Medium

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Three positive numbers form an increasing $G.P.$ If the middle term in this $G.P.$ is doubled,the new numbers are in $A.P.$ Then the common ratio of the $G.P.$ is:

DifficultJEE MAIN 2014

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If $a, b, c$ are in $A.P.$ and $a^2, b^2, c^2$ are in $H.P.$,then

DifficultIIT 2003

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If $A$ and $G$ are the arithmetic mean and geometric mean of $a$ and $b$ respectively,then what is the value of $A - G$?

Easy

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If the arithmetic mean of two positive numbers is $A$,their geometric mean is $G$,and their harmonic mean is $H$,then $H$ is equal to:

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The $A.M., H.M.$ and $G.M.$ between two numbers are $\frac{144}{15}$,$15$ and $12$,but not necessarily in this order. Then $H.M., G.M.$ and $A.M.$ respectively are

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