The ratio of sum of $m$ and $n$ terms of an $A.P.$ is ${m^2}:{n^2}$, then the ratio of ${m^{th}}$ and ${n^{th}}$ term will be
$\frac{{m - 1}}{{n - 1}}$
$\frac{{n - 1}}{{m - 1}}$
$\frac{{2m - 1}}{{2n - 1}}$
$\frac{{2n - 1}}{{2m - 1}}$
Let ${T_r}$ be the ${r^{th}}$ term of an $A.P.$ for $r = 1,\;2,\;3,....$. If for some positive integers $m,\;n$ we have ${T_m} = \frac{1}{n}$ and ${T_n} = \frac{1}{m}$, then ${T_{mn}}$ equals
If the ratio of the sum of $n$ terms of two $A.P.'s$ be $(7n + 1):(4n + 27)$, then the ratio of their ${11^{th}}$ terms will be
Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$
If $\frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b,$ then find the value of $n$.
If the sum of the series $54 + 51 + 48 + .............$ is $513$, then the number of terms are