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

Given that $n$ arithmetic means are inserted between two sets of numbers $(a, 2b)$ and $(2a, b)$,where $a, b \in \mathbb{R}$. Suppose the $m^{th}$ means between these sets are equal,then the ratio $a : b$ is equal to:

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:

If the $n$ terms $a_1, a_2, \ldots, a_n$ are in $A$.$P$. with common difference $r$,then the difference between the mean of their squares and the square of their mean is

The interior angles of a polygon with $n$ sides are in an $A.P.$ with a common difference of $6^{\circ}$. If the largest interior angle of the polygon is $219^{\circ}$,then $n$ is equal to . . . . . .

The first term of an $A$.$P$. of $30$ non-negative terms is $\frac{10}{3}$. If the sum of this $A$.$P$. is the cube of its last term,then its common difference is: