The reciprocal of the mean of the reciprocals of $n$ observations is their
$A.M.$
$G.M.$
$H.M.$
None of these
Let the first three terms $2, p$ and $q$, with $q \neq 2$, of a $G.P.$ be respectively the $7^{\text {th }}, 8^{\text {th }}$ and $13^{\text {th }}$ terms of an $A.P.$ If the $5^{\text {th }}$ term of the $G.P.$ is the $\mathrm{n}^{\text {th }}$ term of the $A.P.$, then $\mathrm{n}$ is equal to
Suppose $a,\,b,\,c$ are in $A.P.$ and ${a^2},{b^2},{c^2}$ are in $G.P.$ If $a < b < c$ and $a + b + c = \frac{3}{2}$, then the value of $a$ is
If $A$ and $G$ are arithmetic and geometric means and ${x^2} - 2Ax + {G^2} = 0$, then
If $A . M$. and $G M$. of two positive numbers $a$ and $b$ are $10$ and $8 , $ respectively, find the numbers.
If $a,\;b,\;c$ are in $H.P.$, then for all $n \in N$ the true statement is