Q. 73.7( 3 Votes )

How many three - digit natural numbers are divisible by 9?

Answer :

The three digit natural numbers divisible by 9 are 108, 117, 126, …., 999.

This forms an AP with first term a = 108


and common difference = d = 9


Last term is 999.


Now, number of terms in this AP are given as:


999 = a + (n - 1)d


999 = 108 + (n - 1)9


999 - 108 = 9n - 9


891 + 9 = 9n


900 = 9n


n = 100


Therefore 999 is the 100th term in the AP.


There are 100 three - digit natural numbers that are divisible by 9.


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