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प्रश्न
How many three-digit numbers are divisible by 9?
संख्यात्मक
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उत्तर
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 contain 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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