The sequence $\frac{5}{{\sqrt 7 }}$, $\frac{6}{{\sqrt 7 }}$, $\sqrt 7 $, ....... is

Let $S_{1}$ be the sum of first $2 n$ terms of an arithmetic progression. Let, $S_{2}$ be the sum of first $4n$ terms of the same arithmetic progression. If $\left( S _{2}- S _{1}\right)$ is $1000,$ then the sum of the first $6 n$ terms of the arithmetic progression is equal to:

If ${A_1},\,{A_2}$ be two arithmetic means between $\frac{1}{3}$ and $\frac{1}{{24}}$ , then their values are

If the sum of three consecutive terms of an $A.P.$ is $51$ and the product of last and first term is $273$, then the numbers are

If sum of $n$ terms of an $A.P.$ is $3{n^2} + 5n$ and ${T_m} = 164$ then $m = $

Let $x _1, x _2 \ldots ., x _{100}$ be in an arithmetic progression, with $x _1=2$ and their mean equal to $200$ . If $y_i=i\left(x_i-i\right), 1 \leq i \leq 100$, then the mean of $y _1, y _2$, $y _{100}$ is