The first term of a harmonic progression is $1/7$ and the second term is $1/9$. The $12^{th}$ term is

If $S_1, S_2, S_3, \dots, S_m$ are the sums of $n$ terms of $m$ arithmetic progressions $(A.P.)$ whose first terms are $1, 2, 3, \dots, m$ and common differences are $1, 3, 5, \dots, 2m - 1$ respectively,then $S_1 + S_2 + S_3 + \dots + S_m = $

If five $G.M.s$ are inserted between $486$ and $2/3$,then the fourth $G.M.$ will be:

The sum of the first $n$ terms of an $A.P.$ is given by $S_n = 2n + 3n^2$. Another $A.P.$ is formed with the same first term and double the common difference. The sum of the first $n$ terms of this new $A.P.$ is:

If ${A_1}, {A_2}$; ${G_1}, {G_2}$ and ${H_1}, {H_2}$ are $AMs$,$GMs$,and $HMs$ between two quantities,then the value of $\frac{{G_1 G_2}}{{H_1 H_2}}$ is

$\frac{1^3 + 2^3 + 3^3 + 4^3 + \dots + 12^3}{1^2 + 2^2 + 3^2 + 4^2 + \dots + 12^2} = $