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How Many Three-digit Numbers Are Divisible by 87? - Mathematics

Sum

How many three-digit numbers are divisible by 87?

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Solution

The three-digit number divisible by 87 are as follow 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

`t_n = a + (n - 1)d`

`=> 957 = 174 + (n - 1)(87)`

`=> 783 = (n - 1) xx 87`

=> 9 = n - 1

=> n = 10

Thus 10 three digit numbers are divisble by 87.

Concept: Arithmetic Progression - Finding Their General Term
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 10 Arithmetic Progression
Exercise 10 (B) | Q 6 | Page 140
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