Mathematics

How many three digit numbers are divisible by 9 ?

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

The above series is in A.P. with a = 108, d = 117 - 108 = 9 and l = 999.

Let the nth term be last term

∴ a_n = 999.

We know that

a_n = a + (n - 1)d

⇒ 999 = 108 + (n - 1) × 9
⇒ 108 + 9n - 9 = 999
⇒ 9n + 99 = 999
⇒ 9n = 900
⇒ n = 100.

Hence, 100 three digit numbers are divisible by 9.

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