The product of $n$ positive numbers is $1$. The sum of these numbers cannot be less than what value?

If $a, b,$ and $c$ are in both Arithmetic Progression $(AP)$ and Geometric Progression $(GP)$,then........

If $x, 1, z$ are in $A.P.$ and $x, 2, z$ are in $G.P.$,then $x, 4, z$ will be in

If the first and $(2n - 1)^{th}$ terms of an $A.P.$,$G.P.$,and $H.P.$ are equal and their $n^{th}$ terms are respectively $a, b$ and $c$,then:

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

Suppose $a, b, c$ are in $A.P.$ and $a^{2}, 2b^{2}, c^{2}$ are in $G.P.$ If $a < b < c$ and $a+b+c=1,$ then $9(a^{2}+b^{2}+c^{2})$ is equal to . . . . . . .