Question
How many three-digit numbers are divisible by 9?
✓
Answer
The two-digit numbers divisible by 9 start from
108, 117, 126, 135, ..., 999
Here,
$a = 108$
$d = 9$
$a_n = a + (n - 1)d$
$\Rightarrow 999 = 108 + (n - 1)(9)$
$\Rightarrow 999 = 108 + 9n - 9$
$\Rightarrow 900 = 9n$
$\Rightarrow n = 100$
This, 100 two-digit number are divisible by 9.
108, 117, 126, 135, ..., 999
Here,
$a = 108$
$d = 9$
$a_n = a + (n - 1)d$
$\Rightarrow 999 = 108 + (n - 1)(9)$
$\Rightarrow 999 = 108 + 9n - 9$
$\Rightarrow 900 = 9n$
$\Rightarrow n = 100$
This, 100 two-digit number are divisible by 9.
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