# Very-Short and Short-Answer Questions

Question:

Very-Short and Short-Answer Questions

How many three-digit natural numbers are divisible by 7?

Solution:

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

Clearly, these number are in AP.

Here, = 105 and d = 112 − 105 = 7

Let this AP contains n terms. Then,

$a_{n}=994$

$\Rightarrow 105+(n-1) \times 7=994 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow 7 n+98=994$

$\Rightarrow 7 n=994-98=896$

$\Rightarrow n=128$

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