Question

How many three-digit natural numbers are divisible by 9?

Answer 1

The three-digit natural numbers divisible by 9 are 108, 117, 126 ,….. 999.
Clearly, these number are in AP.
Here. a = 108 and d = 117 – 108 = 9
Let this AP contains n terms. Then,

a_n = 999

⇒ 108 +(n-1) × 9 = 999               [a_n  = a+(n-1) d]

⇒ 9n + 99 = 999

⇒ 9n = 999- 99 =900

⇒ n = 100

Hence, there are 100 three-digit numbers divisible by 9.