Question

The sum of all the three digit numbers that leave a remainder of 3 when divided by 4 is___.

Answer 1

The smallest three digit number that leave a remainder of 3 when divided by 4 = 103.
The largest three digit number that leave a remainder of 3 when divided by 4 = 999.
$T_n=a+(n-1)d$
999 = 103 + (n -1) 4
n = 225
$S_n=\left(\frac{n}{2}\right)$ (First term +Last term)
$=\left(\frac{225}{2}\right)(103+999)$
= 123975