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Question
How many three-digit numbers are divisible by 9?
Solution
The three-digit numbers divisible by 9 are 108, 117, 126,...., 999.
Clearly, these number are in AP.
Here. a = 108 and d = 117 – 108 = 9
Let this AP contains n terms. Then.
an = 999
⇒ 108 + (n-1) × 9 = 999 [an = a + (n-1) d ]
⇒ 9n + 99 =999
⇒ 9n = 999 -99=900
⇒ n = 100
Hence: there are 100 three-digit numbers divisible by 9.
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