Question

Find the sum of all natural numbers between 100 and 1000 which are multiples of 5.

Answer 1

Natural numbers b/w 100 and 1000 which are multiples of 5 are :

$105,110,115,.........,990,995$.

$a=105$, $d=5$

$a_n=995$

$a+(n-1)d=995$

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

$(n-1)5=890$

$n-1=178$

$n=179$

Hence,

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

$S_{179}=\frac{179}{2}[210+890]$

$S_{179}=\frac{179}{2}\times 1100=98450$