Question
How many two digit numbers are divisible by $3?$
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Answer
The two digit numbers divisible by $3$ are as follows:
$12,15,18,21,............,99$
Clearly, this forms an A.P with first term, $a = 12$
and common difference, $d = 3$
Last term $= n^{th}$ term $= 99$
The general term of an A.P is given by
$t_n = a + (n - 1)d$
$\Rightarrow 99=12+(n-1)(3)$
$\Rightarrow 99=12+3 n-3$
$\Rightarrow 90=3 n$
$\Rightarrow n =30$
Thus, $30$ two digit numbers are divisible by $3.$
$12,15,18,21,............,99$
Clearly, this forms an A.P with first term, $a = 12$
and common difference, $d = 3$
Last term $= n^{th}$ term $= 99$
The general term of an A.P is given by
$t_n = a + (n - 1)d$
$\Rightarrow 99=12+(n-1)(3)$
$\Rightarrow 99=12+3 n-3$
$\Rightarrow 90=3 n$
$\Rightarrow n =30$
Thus, $30$ two digit numbers are divisible by $3.$
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