Question

How many three-digit numbers are divisible by 7?

Options

• 112

• 114

• 128

• 110

Answer 1

128

Explanation:-

We have an AP starting at 105 because it is the first three digit number divisible by 7.

AP will end at 994 because it is the last three digit number divisible by 7.

Therefore, we have an AP 105,112,119…994

First term, a = 105

Common difference, d = 112 - 105 = 7

Using formula a_n = a + (n - 1)d, to find n^th term of arithmetic progression, we can say that

994 = 105 + (n - 1)(7)

⇒ 994 = 105 + (n - 1)(7)

⇒ 889 = 7(n - 1)

⇒ n - 1 = `889/7`

⇒ n = 127 + 1 =128

994 is the 128^th term of AP. Therefore, there are 128 terms in AP. In other words, we can also say that there are 128 three digit numbers divisible by 7.