The given sequence is: 5, 15, 6, 18, 7, 21, 8.
To determine the next number in this sequence, let’s analyze the pattern:
- The first and second numbers are 5 and 15.
- Then the sequence alternates: 5 to 6 (increasing by 1), and 15 to 18 (increasing by 3).
- This pattern continues with 6 to 7 (again increasing by 1), and 18 to 21 (increasing by 3).
Observing these increments:
- The odd-positioned numbers (1st, 3rd, 5th, 7th) are increasing by 1: 5, 6, 7, 8. The next odd position number would be 9.
- The even-positioned numbers (2nd, 4th, 6th) are increasing by 3: 15, 18, 21. The next even position number would be 24.
Thus, the next number in the sequence, following the identified pattern, would be 24 after 8.
So the complete sequence continuing with the appropriate pattern would be: 5, 15, 6, 18, 7, 21, 8, 24.