How many three digit numbers are divisible by 7?

Three digits numbers divisible by 7 are,

105, 112, 119, …….., 994.

Let 994 be n^th term.

⇒ a_n = a + (n - 1)d

⇒ 994 = 105 + (n - 1)7

⇒ 994 - 105 = 7(n - 1)

⇒ 7(n - 1) = 889

⇒ n - 1 = 127

⇒ n = 128.

Hence, 128 three digit numbers are divisible by 7.