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

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

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.

To identify the next numbers in the pattern 1, 2, 5, 11, 21, let's analyze the differences between consecutive terms:

The difference between 2 and 1 is 1.
The difference between 5 and 2 is 3.
The difference between 11 and 5 is 6.
The difference between 21 and 11 is 10.

We observe that the differences are increasing by consecutive odd numbers: 1, 3, 5, and so on. This indicates that the pattern might involve the concept of adding consecutive odd numbers to each term.

To verify this, we can continue the pattern by adding the next odd number to the last term, which is 10:

21 + 10 = 31.

Therefore, the next number in the pattern is 31.

To summarize, the pattern 1, 2, 5, 11, 21 follows the rule of adding consecutive odd numbers to each term.