What is the sum of all numbers between $100$ and $300$ that are divisible by $7$?

The common difference of the $A.P.: a_{1}, a_{2}, ..., a_{m}$ is $13$ more than the common difference of the $A.P.: b_{1}, b_{2}, ..., b_{n}$. If $b_{31} = -277$, $b_{43} = -385$ and $a_{78} = 327$, then $a_{1}$ is equal to

If $1, \log_{y}x, \log_{z}y, -15\log_{x}z$ are in $A.P.$,then

If the sum of $n$ terms of an $A.P.$ is $S_n = nP + \frac{1}{2}n(n-1)Q$,where $P$ and $Q$ are constants,find the common difference.

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:

The sum of all integers between $1$ and $100$ (both inclusive) which are divisible by $5$ or $13$ is