Find the sum of all $\displaystyle 3$-digit natural numbers which are divisible by 11.

$\displaystyle 3$ - digit natural numbers divisible by $\displaystyle 11$ are \[110,121, \ldots, 990 \] Here first term = $\displaystyle 110$ and common difference = $\displaystyle 11$ \[\begin{aligned} & a_{n}=990 \\ \Rightarrow & 110+(n-1) \times 11=990 \\ \Rightarrow & n=81 \\ S_{81}= & \frac{81}{2} \times[110+990] \\ = & 44550 \end{aligned} \]