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Question
How many numbers of two digit are divisible by 3?
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Solution
The two digit numbers that are divisible by 3 are:
12, 15, 18...96, 99
This is an A.P. whose first term is 12 and the common difference is 3.
\[\text { We have }: \]
\[ a_n = 99\]
\[ \Rightarrow 12 + (n - 1)3 = 99\]
\[ \Rightarrow (n - 1)3 = 87\]
\[ \Rightarrow (n - 1) = 29\]
\[ \Rightarrow n = 30\]
Thus, there are 30 such terms.
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