What will be the next digit in the sentence 1, 1, 2, 3, 5, 8, 13, 21, 34?
show me your way of thinking : )

It's Fibonacci :

so you have 
1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Basically, to find out the number:

13=5+8
21=13+8
34=21+13
55=34+21

The next number is the sum of the previous two.