How many three - digit natural numbers are divisible by 7?
The three digit numbers divisible by 7 are 105, 112, 119, …., 994.
This forms an AP with first term a = 105
and common difference = d = 7
Last term is 994.
Now, number of terms in this AP are given as:
994 = a + (n - 1)d
⇒ 994 = 105 + (n - 1)7
⇒ 994 - 105 = 7n - 7
⇒ 889 + 7 = 7n
⇒ 896 = 7n
⇒ n = 128
Therefore 994 is the 128th term in the AP.
∴ There are 128 three - digit natural numbers that are divisible by 7.