Question
How many three-digit numbers are divisible by $87?$
✓
Answer
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 $= n^{th}$ term $= 957$
The general term of an A.P is given by
$t_n=a+(n-1) d$
$\Rightarrow 957=174+(n-1)(87) $
$ \Rightarrow 783=(n-1) \times 87$
$\Rightarrow 9 = n - 1$
$\Rightarrow n = 10$
Thus $10$ three digit numbers are divisble by $87.$
Clearly, this forms an A.P. with the first term $a= 174$ and common difference $d = 87.$
Last term $= n^{th}$ term $= 957$
The general term of an A.P is given by
$t_n=a+(n-1) d$
$\Rightarrow 957=174+(n-1)(87) $
$ \Rightarrow 783=(n-1) \times 87$
$\Rightarrow 9 = n - 1$
$\Rightarrow n = 10$
Thus $10$ three digit numbers are divisble by $87.$
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