If A_1, A_2 are the two A.M.'s between two nu | vedclass

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(A) Given that $a, A_1, A_2, b$ are in $A.P.$The sum of $A.M.'s$ inserted between $a$ and $b$ is given by $A_1 + A_2 = n 	imes \frac{a+b}{2}$,where $

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$\frac{a + b}{ab}$

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(A) Given that $a, A_1, A_2, b$ are in $A.P.$The sum of $A.M.'s$ inserted between $a$ and $b$ is given by $A_1 + A_2 = n 	imes \frac{a+b}{2}$,where $n=2$.So,$A_1 + A_2 = 2 	imes \frac{a+b}{2} = a + b$ .....$(i)$Given that $a, G_1, G_2, b$ are in $G.P.$The product of $G.M.'s$ inserted between $a$ and $b$ is given by $G_1 G_2 = (ab)^{n/2}$,where $n=2$.So,$G_1 G_2 = (ab)^{2/2} = ab$ .....$(ii)$Therefore,$\frac{A_1 + A_2}{G_1 G_2} = \frac{a + b}{ab}$.

If $A_1, A_2$ are the two $A.M.'s$ between two numbers $a$ and $b$ and $G_1, G_2$ are two $G.M.'s$ between the same two numbers,then $\frac{A_1 + A_2}{G_1 G_2} = $

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