(Q5).How many two-digit numbers are divisible by 3?

The list of two-digit numbers divisible by 3 is :

12, , , . . . , 99

Is this an AP ? Yes it is. Here, a = , d = , an = 99.

As an= a + (n – 1) d,

we have = + (n – 1) ×

i.e., = (n – 1) ×

i.e., n – 1 =
=

i.e., n = + 1 = (So, 99 is the th term)

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