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, a = 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.
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