Sum

How many two-digit numbers are divisible by 3?

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#### Solution

The two digit numbers divisible by 3 are as follows:

12, 15, 18, 21, ...., 99

Clearly, this form an A.P with first term a = 12 and common difference d = 3

Last term = nth term = 99

The general term of an A.P is given by

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

=> 99 12 + (n - 1)(3)

=> 99 = 12 + 3n - 3

=> 90 = 3n

=> n = 30

Thus 30 two-digit numbers are divisible by 3.

Concept: Arithmetic Progression - Finding Their General Term

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