Question

Find the sum of all multiples of $5$ lying between $101$ and $999$.

Answer 1

$a=105,a_n=995,d=5$

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

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

$890=(n-1)5$

$n-1=178$

$n=179$

$S_n=\frac{n}{2}[a+l]$

$=\frac{179}{2}[105+995]$

$=\frac{179}{2}\left[1100\right]$

$=179\times 550$

$=98450$