Question

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10. How many three-digit natural numbers are divisible by 7?

Answer 1

Dear student

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 t_n = 994.

n^th term of A.P = t_n = 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.
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