Find the sum of all $3$-digit natural numbers which are multiples of $11$.

Find the sum of the given series.

$18+15\frac{1}{2}+13+...+\left(-49\frac{1}{2}\right)$.

In an A.P. the first term is $8$, $n^{\mathrm{th}}$ term is $33$ and the sum of first $n$ terms is $123$, find $n$ and $d$, the common difference.

Sum of the first $14$ terms of an A.P. is $1505$ and its first term is $10$. Find its ${25}^{\mathrm{th}}$ term.

If $S_n$denotes the sum of first $n$ terms of an A.P., prove that $S_{12}=3(S_8-S_4)$.