Write the first three terms in each of the following sequences defined by the following:
$a_{n} = 2n + 5$

Let the sum of $n, 2n, 3n$ terms of an $A.P.$ be $S_{1}, S_{2}$ and $S_{3}$ respectively. Show that $S_{3} = 3(S_{2} - S_{1})$.

The sum of all natural numbers $n$ such that $100 < n < 200$ and $H.C.F. (91, n) > 1$ is

The first term of an arithmetic progression is $10$ and the last term is $50$. If the sum of all its terms is $300$,then the number of terms $n = ...$

If the middle term of the $AP$ is $300$,then the sum of its first $51$ terms is

If $a, b, c$ are in Arithmetic Progression,then $\frac{1}{\sqrt{b} + \sqrt{c}}, \frac{1}{\sqrt{c} + \sqrt{a}}, \frac{1}{\sqrt{a} + \sqrt{b}}$ are in: