Question

Very-Short and Short-Answer Questions

How many three-digit natural numbers are divisible by 7? [CBSE 2013]

Answer 1

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

Clearly, these number are in AP.

Here, a = 105 and d = 112 − 105 = 7

Let this AP contains n terms. Then,

$$\begin{gathered} a_n=994 \\ \Rightarrow 105+\left(n-1\right)\times 7=994\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow 7n+98=994 \\ \Rightarrow 7n=994-98=896 \\ \Rightarrow n=128 \end{gathered}$$

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