Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 390$ and the ratio of the tenth and the fifth terms is $15:7$,then $S_{15} - S_5$ is equal to:

$a_1, a_2, a_3, \dots, a_{100}$ are in an arithmetic progression,where $a_1 = 3$ and $S_p = \sum_{i=1}^p a_i, 1 \le p \le 100$. For any integer $n$,let $m = 5n$. If $S_m/S_n$ is independent of $n$,then $a_2 = \dots$

If all interior angles of a quadrilateral are in $A.P.$ and the common difference is $10^{\circ}$,find the smallest angle. (in $^{\circ}$)

The sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is $10$,the number of such triangles is

Let $\alpha_{1}, \alpha_{2}, \alpha_{3}, \alpha_{4}$ be an $A$.$P$. of four terms such that each term of the $A$.$P$. and its common difference $l$ are integers. If $\alpha_{1}+\alpha_{2}+\alpha_{3}+\alpha_{4}=48$ and $\alpha_{1}\alpha_{2}\alpha_{3}\alpha_{4}+l^{4}=361$,then the largest term of the $A$.$P$. is equal to

The sum of all those terms of the arithmetic progression $3, 8, 13, \ldots, 373$ which are not divisible by $3$ is equal to $.......$.