How many three-digit numbers are divisible by 7?

List of the three digit numbers divisible by 7 are : 105, 112, 119, ........., 994. The above list is an A.P. with, First term (a) = 105 and common difference (d) = 112 - 105 = 7. Let nth term be 994. By formula, ⇒ a n = a + (n - 1)d ⇒ 994 = 105 + 7(n - 1) ⇒ 994 = 105 + 7n - 7 ⇒ 994 = 7n + 98 ⇒ 7n = 994 - 98 ⇒ 7n = 896 ⇒ n = = 128. Hence, 128 three digit numbers are divisible by 7.