Question

How many three digit numbers are divisible by 7?

Answer 1

The first three digit number which is divisible by 7 is 105 and the last digit which is divisible by 7 is 994.

This is an A.P. in which a = 105, d = 7 and t_n = 994.

We know that n^th term of A.P is given by

 t_n = a + (n – 1)d

`\implies` 994 = 105 + (n – 1)7

`\implies` 889 = 7n – 7

`\implies` 896 = 7n

`\implies` n = 128

∴ There are 128 three digit numbers which are divisible by 7.