# How many two digits numbers are divisible by 3?

1st two-digit number which is divisible by 3 is 12.

2nd two-digit number which is divisible by 3 is 15.

3rd two-digit number which is divisible by 3 is 18.

Last two-digit number which is divisible by 3 is 99.

12, 15, 18, ……, 99
This is an AP as the difference between the consecutive numbers is the same.
15 - 12 = 18 - 15 = 3
We know the nth term of AP is given by:

an = a + (n – 1) d

⇒ 99 = 12 + (n – 1)3
⇒ 99 = 12 + 3n - 3

⇒ 99 = 9 + 3n
⇒ 99 - 9 = 3n
⇒ 90 = 3n

⇒ n = 30

So, there are 30 two-digit numbers which are divisible by 3.

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