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Question
How many three-digit numbers are divisible by 87?
Solution
The three-digit numbers divisible by 87 are as follows.
174, 261, ....., 957
Clearly, this forms an A.P. with the first term a = 174 and common difference d = 87.
Last term = nth term = 957
The general term of an A.P. is given by
tn = a + (n – 1)d
`=>` 957 = 174 + (n – 1)(87)
`=>` 783 = (n – 1) × 87
`=>` 9 = n – 1
`=>` n = 10
Thus, 10 three-digit numbers are divisible by 87.
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