Question

Find the sum of all natural numbers lying between $100$ and $1000$, which are multiples of $5$

Answer 1

Multiples of $5$ are $5,10,15,.....$

between $100$ & $1000$ are $105,1,0,\dots \dots \dots .,995$

$a=105$

$d=5$

$l=995$

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

$\Rightarrow 995=105+(n-1)5$

$\Rightarrow 995=100\pm 5(n-1)$

$\Rightarrow 895=5n$

$\Rightarrow n=179$

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

$=\frac{179}{2}[2\times 105+(179-1)\times 5]$

$=179\times 550$

$=98450$

Sum is $98450$.