Question

Find how many two digit numbers are divisible by 3

Answer 1

I'll use arithmetic series to find it.

First two-digit number divisible by 3 is 12, last such number is 99. Every 3rd number is divisible by 3.

So,

$a_1=12\\a_n=99\\d=3\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=12+(n-1)\cdot 3\\3n-3=87\\3n=90\\n=30$

There are 30 such numbers.