Question

How many three digit numbers are divisible by 7?

 

Answer 1

In this problem, we need to find out how many numbers of three digits are divisible by 7.

So, we know that the first three digit number that is divisible by 7 is 105 and the last three digit number divisible by 7 is 994. Also, all the terms which are divisible by 7 will form an A.P. with the common difference of 7.

So here,

First term (a) = 105

Last term (a_n) = 994

Common difference (d) = 7

So, let us take the number of terms as n

Now, as we know,

a_n = a + (n-1)d 

So, for the last term,

      994 = 105 + (n-1) 7 

      994 = 105 + 7n - 7

       994 = 98 + 7 n

994 - 98 = 7 n

Further simplifying,

896 = 7 n

   `n = 896/7`

    n = 128

Therefore, the number of three digit terms divisible by 7 is128.