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 = $\dfrac{896}{7}$ = 128.

Hence, 128 three digit numbers are divisible by 7.