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

The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ 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 ratio of the sums of $m$ and $n$ terms of an $A.P.$ is $m^{2}: n^{2}$. Show that the ratio of the $m^{th}$ and $n^{th}$ term is $(2m-1):(2n-1)$.

$a_1, a_2, a_3, \dots, a_{100}$ 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 $p$ times the $p^{th}$ term of an $A.P.$ is equal to $q$ times the $q^{th}$ term of an $A.P.$,then the $(p + q)^{th}$ term is