Find the sum of all integers between 100 and 550,

The integers between 100 and 550 that are divisible by 9 are:

108, 117...549

Here, we have:

$a=108$

$d=9$

$a_{n}=549$

$\Rightarrow 108+(n-1)(9)=549$

$\Rightarrow 9 n-9=441$

$\Rightarrow 9 n=450$

$\Rightarrow n=50$

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

$\Rightarrow S_{50}=\frac{50}{2}[2 \times 108+(50-1) \times 9]$

$\Rightarrow S_{50}=25(657)=16425$