Question

How many three digit number are divisible by 9?

Answer 1

the lowest number greater than a hundred and divisible by 9 is 108...
the largest number divisible by 9 and less than a thousand is 999...

we use this formula...

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

$a_n$ is the nth term in an arithmetic sequence
a is the first term in an arithmetic sequence
n is the number of terms
d is the common difference


first term(a) = 108
last term($a_n$ ) = 999
common difference(d) = 9

we substitute the given values

999 = 108 + ( n - 1 ) $\times$ 9

we then solve...
999 = 108 + ( n - 1 ) $\times$ 9
999 - 108 = ( n - 1 ) $\times$ 9
891 = ( n - 1 ) $\times$ 9
$\frac{891}{9}=\frac{\left[\right(n-1)\times 9]}{9}$
99 = n - 1
99 + 1 = n
100 = n

there are 100 3-digit numbers divisible by 9.