Question

Find the sum of integers which are divisible by $5$ from $1$ to $100$

Answer 1

Numbers divisible by $5$ are $5,10,15,20,\mathrm{25.........100}$.
Now, we have to find the sum of these numbers
$\Rightarrow 5+10+15+\mathrm{20..............}+100$
can be written as
$\Rightarrow 5(1+2+3+....................+20)$
Using the formula, sum of first $n$ numbers $=\frac{n(n+1)}{2}$
$=5\left(\frac{20\left(21\right)}{2}\right)$

$=5\times 210=1050$

Therefore, sum of integers which are divisible by $5$ from $1$ to $100$ is $1050$.