Question

Find the sum of all odd numbers of four digits which are divisible by $9$.

Answer 1

The four-digit odd numbers that are divisible by $9$ are $1017,1035,..9999$

The sequence forms an $AP$ with $a=1017,d=18$

$L$ is the last term of the series.

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

$9999=1017+(n-1)18$

$n=500$

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

$S_{500}=\frac{500}{2}(1017+9999)=2754000$