To Find : 2 – digit numbers divisible by 3.
First 2 – digit number divisible by 3 is 12
Second 2 – digit number divisible by 3 is 15 and
Last 2 – digit number divisible by is 99.
Given: The AP is 12, 15, 18,…………..,99
a1 = 12, a2 = 15, d = 15–12 = 3 and an = 99
(Where a=a1 is First term, a2 is Second term, an is nth term and d is common difference of given AP)
Formula Used: an = a + (n – 1)d
99 = 12 + (n – 1)3
87 = (n – 1)3
29 = (n – 1)
n = 30

So, There are total of 30 two – digit number which is divisible by 3.