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Question
How many three-digit natural numbers are divisible by 9?
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Solution
The three-digit natural 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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