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Question
How many three-digit numbers are divisible by 7?
Solution
Is a list of three-digit numbers divisible by 7.
105, 112, 119, …, 994
a = 105, d = 112 - 105 = 7, an = 994
∴ an = a + (n - 1)d
⇒ 994 = 105 + (n - 1) × 7
⇒ 994 = 105 + 7n - 7
⇒ 7n = 994 + 7 - 105
⇒ 7n = 1001 - 105
⇒ 7n = 896
⇒ n = `896/7`
⇒ n = 128
Hence, there are 128 three-digit numbers divisible by 7.
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