How do you find the rule to this sequence 1,2,3,5,8,13,21. Is it the Fibonacci sequence?

Yes, it's the Fibonacci series.

(The first two terms are missing. If you want to start it from the very beginning,

then you need another 0, 1, before the part that we can see in your question.)

The rule is:

Each term is the sum of the two terms before it. In order to get a new one,

add up the last two terms that you already have.

You want to subract your last two numbers and keep going to find a common number