Find the sum of all natural numbers that are less than 100 and divisible by 4.

To do:  The sum of all natural numbers that are less than 100 and divisible by 4

Solution:

The smallest natural number divisible by 4 is 4
The largest number within 100  which is divisible by 4 is  96
Thus, first term, a=4
Common difference is d=8-4=4

We will find the total number , n=?
$a_n=96$

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

$96=4+(n-1)4$

$96-4=4n-4$

$92+4=4n$

$96=4n$

$n=\frac{96}{4}$

$n=24$

We can directly find n by directly multiplying $\frac{96}{4}$

Now,

$S_n=\frac{n}{2}\times (a+a_n)$

$S_n=\frac{24}{2}\times (4+96)$

$S_n=\frac{24}{2}\times 100$

$S_n= 12\times 100$

So when we do it,we get

$S_n=1200$