How many numbers of two digit are divisible by 3?

To do:

We have to find the number of two digits divisible by 3.

Solution:

Let $n$ be the number of terms which are divisible by $3$.

Let $a$ be the first term and $d$ be the common difference.

The first two-digit number divisible by $3$ is $12$.

This implies,

$a = 12, d = 3$, last term $a_n = 99$

$a_n = a + (n – 1) d$

$99 = 12 + (n – 1) \times 3$

$99- 12 = 3n – 3$

$3n = 87 +3$

$3n = 90$

$n=\frac{90}{3}$

$n=30$

Therefore, 30 two-digit numbers are divisible by 3.