Question

How many three-digit numbers are divisible by 7?

Answer 1

Is a list of three-digit numbers divisible by 7.

105, 112, 119, …, 994

a = 105, d = 112 - 105 = 7, a_n = 994

∴ a_n = a + (n - 1)d

⇒ 994 = 105 + (n - 1) × 7

⇒ 994 = 105 + 7n - 7

⇒ 7n = 994 + 7 - 105

⇒ 7n = 1001 - 105

⇒ 7n = 896

⇒ n = `896/7`

⇒ n = 128

Hence, there are 128 three-digit numbers divisible by 7.