Find the sum of all natural numbers lying between $100$ and $1000$ which are multiples of $5.$

If the sum of $n$ terms of an $AP$ is given by $S_{n} = n^{2} + n$,then the common difference of the $AP$ is

For $n \in N$,what is the value of $1+4+7+\cdots+(3n-2)$?

If $\frac{S_n}{S_m} = \frac{n^4}{m^4}$ (where $S_k$ is the sum of the first $k$ terms of an $A$.$P$. $a_1, a_2, \dots$),then the value of $\frac{a_{m+1}}{a_{n+1}}$ in terms of $m$ and $n$ is:

If $\frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b,$ then find the value of $n$.

Let $a_{1}, a_{2}, a_{3}, \ldots$ be an $A.P.$ If $\frac{a_{1}+a_{2}+\ldots+a_{10}}{a_{1}+a_{2}+\ldots+a_{p}}=\frac{100}{p^{2}}, p \neq 10$,then $\frac{a_{11}}{a_{10}}$ is equal to :