Three digit numbers divisible by 7 : 105, 112, 119, . . . , 994
Let the total number of these numbers be n.
Here, a = 105 and d = 112 – 105 = 7. To find: n, where a_n = 994.
Given that: a_n = a + (n – 1)d = 994
⇒ 105 + (n -1)(7) = 994
⇒ 7(n -1) = 889
⇒ n – 1 = 888/7 = 127 ⇒ n = 128
Hence, there are 128 three digits numbers which are divisible by 7.