Question

how many 3 digits number are divisible by 7

Answer 1

The first three digit number which is divisible by 7 is 105 and last three digit number which is divisible by 7 is 994.

This is an A.P. in which a = 105, d = 7 and l = 994.

Let the number of terms be n . Then tn = 994.

nth term of A.P = tn = a + (n - 1)d.

⇒ 994 = 105 + (n -1)7.

⇒ 889 = 7(n-1)

⇒ n -1 = 127

∴ n = 128.

∴ There are128 three digit numbers which are divisible by 7.

Answer 2

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The three digits number divisible by 7 are: 105,112....,994

So we have, an= 994, a= 105, d= 7

We have to find n

So an= a+(n-1)d

994 = 105 + 7n-7

994-105= 7n-7

889+7= 7n

896= 7n

n= 896/7

n= 128