Question

How many three-digit numbers are divisible by 9?

Answer 1

The three-digit 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 contain 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.