1, 2, 11, 31, ?

[sinn]

1, 2, 11, 31, ?

A simple pattern that fits well is to look at the differences:

• 2 − 1 = 1
  
• 11 − 2 = 9
  
• 31 − 11 = 20
  

Now look at how those differences change:

• 9 − 1 = 8
  
• 20 − 9 = 11
  

Those “second differences” go +8, +11.
If that pattern continues, the next jump would be +14 (increasing by 3 each time).
So the next difference becomes:
20 + 14 = 34
Then the next term is:
31 + 34 = 65
Answer: 65
If you want, we can explore alternative patterns too, but this is the cleanest one.