Question

Which numbers comes next in the patterns 1,2,5,11,21

Answer 1

taking differences
1
2 1
5 3 2
11 6 3 1
21 10 4 1

the third differences are constant, so we could represent it as a cubic function.
Lots of work, so I went to Wolfram:

http://www.wolframalpha.com/input/?i=pattern+%7B1,2,5,11,21,....%7D

Answer 2

57
solution
1,2,5,11,21
2-1=1
5-2=3
11-5=6
21-11=10

3-1=2
6-3=3
10-6=4

if you observe, the first one it was added by 2 when it got to 6 it was added by 3 and to arrive at 10, it was added by 4
so therefore, the next sequence will be added by 5 that's what brings about the second solving
when you add 10 to 5 you'll get 15
therefore, 15 +21=36
1 2,5,11,21,36.

If you don't understand it well Koone call me so I can explain better. my number is 08109596025.