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How many numbers of two digit are divisible by 3?
We have to find the number of two digits divisible by 3.
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 $12$.
$a = 12, d = 3$, last term $a_n = 99$
$a_n = a + (n – 1) d$
$99 = 12 + (n – 1) \times 3$
$99- 12 = 3n – 3$
$3n = 87 +3$
$3n = 90$
Therefore, 30 two-digit numbers are divisible by 3.
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