The next number in the series 3, 6, 9, 15, 24, 39 is 63.

This sequence follows a recursive pattern where each term is the sum of the previous term and the one before that, starting after the initial terms. Specifically, it begins with 3, 6, 9, then 15 = 9 + 6, 24 = 15 + 9, 39 = 24 + 15, and thus the next is 39 + 24 = 63.

Pattern Breakdown

Examine the differences between consecutive terms, which mirror the sequence itself:

  • 6 - 3 = 3
  • 9 - 6 = 3
  • 15 - 9 = 6
  • 24 - 15 = 9
  • 39 - 24 = 15
  • Next difference: 24 , so 39 + 24 = 63

Term Position| Number| Calculation
---|---|---
1| 3| Starting value
2| 6| Starting value
3| 9| Starting value
4| 15| 9 + 6
5| 24| 15 + 9
6| 39| 24 + 15
7| 63| 39 + 24 13

Why This Pattern Fits

This Fibonacci-like addition (every term as prior two summed) aligns with common puzzle logic seen in math forums and study sites. Other guesses like 48 or 51 appear in discussions but fail the consistent recursion test.

TL;DR: 63, via the recursive sum pattern confirmed across math resources.