Question

How many 3-digit numbers are divisible by 7?

Answer 1

The smallest three-digit number which is divisible by 7 is 105 and the largest three-digit number divisible by 7 is 994.
Hence, the progression is 105, 112, 119,..., 994
Here, a = 105, d = 7 and last term = 994
Let n be the number of terms of the sequence.
Now, we have:
T_n = 994 ⇒ a + (n - 1)d = 994
⇒ 105 + (n - 1) ⨯ 7 = 994
⇒ 7n-7 = 889
⇒ 7n = 896
⇒ n = 128

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