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How Many Numbers of Two Digit Are Divisible by 3? - Mathematics

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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.2 | Q 18 | Page 12
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