Identifying the Series Pattern

The given sequence is: 0, 1, 2, 3, 6, 11, 20, 37, 68, ...

This series does not follow a simple arithmetic or geometric rule. It is a recursive sequence where each new term is the sum of the three terms that come before it.

Verifying the Pattern

Let's check this rule against the numbers in the series:

• 0 + 1 + 2 = 3 (the 4th term)
• 1 + 2 + 3 = 6 (the 5th term)
• 2 + 3 + 6 = 11 (the 6th term)
• 3 + 6 + 11 = 20 (the 7th term)
• 6 + 11 + 20 = 37 (the 8th term)
• 11 + 20 + 37 = 68 (the 9th term)

The pattern is consistent throughout the series.

Calculating the Next Term

To find the next number, we add the last three terms of the sequence:

Next Term = 20 + 37 + 68

Next Term = 57 + 68

Next Term = 125

Conclusion

The number that comes next in the series is 125.