Question

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

Answer 1

The smallest natural number divisible by $4=4$

The largest number inside $100\times 96$

Thus $a=4$

$d=8-4=4$

$n=?$

$a_n=96$

$\Rightarrow a+(n-1)d=96$

$\Rightarrow 4+(n-1).4=96$

$\Rightarrow (n-1)4=96-4$

$\Rightarrow (n-1)4=92$

$\Rightarrow n-1=92/4$

$\Rightarrow n-1=23$

$\Rightarrow n=23+1$

$\Rightarrow n=24$

Now,

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

$Sn=\frac{24}{2}\left[2\right(4)+(24-1\left).4\right]$

$\Rightarrow S_n=12[8+23.4]$

$\Rightarrow S_n=12[8+92]$

$\Rightarrow S_n=12\times 100$

$\Rightarrow S_n=1200$

$\therefore$ Sum of all natural numbers. $S_n=1200$.