Question

How many three digit natural numbers are divisible by 7 ?

Answer 1

The three-digit natural numbers divisible by 7 are 105, 112, 119,.., 994.

Clearly, these numbers are in AP.

Here, a = 105 and d = 112-105 = 7

Let this AP contains n terms. Then,

$a_n=994$

=> 105 + (n-1) $\times$ 7 = 994

=> 7n +98 = 994

=> 7n = 994-98 = 896

=> n = 128

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