Question

Find the sum of all even integers between 100 and 550 , which are divisible by 9.

Answer 1

The series follows as below,

$108,117,...........,549$

Clearly,

$a=108$

$d=117-108=9$

$a_n=a+(n-1)d$

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

$441=9(n-1)$

$49=n-1$

$n=50$

Therefore there are 50 numbers

$S_n=\frac{n}{2}[a+l]$

$S_{50}=\frac{50}{2}[108+549]$

$=25\left[657\right]$

$=16425$