Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$

Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic progression. If $S_{3n} = 3S_{2n}$,then the value of $\frac{S_{4n}}{S_{2n}}$ is:

Three positive numbers $a, b,$ and $c$ are in an Arithmetic Progression $(AP)$ and $abc = 4$. The minimum possible value of $b$ is:

The $8^{th}$ term of the series $2\sqrt{2} + \sqrt{2} + 0 + \dots$ will be: (in $\sqrt{2}$)

If $a_r > 0, r \in N$ and $a_1, a_2, a_3, ..., a_{2n}$ are in an arithmetic progression,then $\frac{a_1 + a_{2n}}{\sqrt{a_1} + \sqrt{a_2}} + \frac{a_2 + a_{2n-1}}{\sqrt{a_2} + \sqrt{a_3}} + \frac{a_3 + a_{2n-2}}{\sqrt{a_3} + \sqrt{a_4}} + ... + \frac{a_n + a_{n+1}}{\sqrt{a_n} + \sqrt{a_{n+1}}} = ?$

If the sum of the $10$ terms of an $A.P.$ is $4$ times the sum of its $5$ terms,then the ratio of the first term to the common difference is: