If the ratio of two numbers be $9:1$, then the ratio of geometric and harmonic means between them will be

Consider an arithmetic series and a geometric series having four initial terms from the set $\{11,8,21,16,26,32,4\}$ If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these two series is equal to .......

If the $2^{nd}\,, \,5^{th}\,\, and \,\,9^{th}$ terms of a non-constant $A.P.$ are in $G.P.$, then the common ratio of this $G.P.$ is :

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

If $m$ is the $A.M$ of two distinct real numbers $ l$  and $n (l,n>1) $ and  $G_1, G_2$ and $G_3$ are three geometric means between  $l$ and $n$ then $G_1^4 + 2G_2^4 + G_3^4$ equals :

If $a,\;b,\;c$ are in $H.P.$, then for all $n \in N$ the true statement is