The number of multiples of $9$  between $1$  to $1000$  is

$9$  multiples are $9,18,27,36,\mathrm{.......},999$

$a=9,d=9$

Let $a_n=999$

$a+\left(n-1\right)d=999$

$9+\left(n-1\right)9=999$

$9n=999$

$n=111$