Question

Find the sum of all three digit numbers which are divisible by 9.

Answer 1

Given that the three digit numbers which are divisible by $9$ are

$108,117,126,...999$

Here $a=108,d=117-108=9$

$\therefore n=\frac{l-a}{d}+1=\frac{999-108}{9}+1=\frac{899}{9}+1=99+1=100$

$\therefore S_{100}=\frac{100}{2}[108+999]=50\times 1107=55,350$