The missing number in the series 5, 6, 9, 15 is 25.
Understanding the Pattern
The series follows a specific pattern of addition, where the amount added increases with each step. Let's break down how this works:
- Step 1: 5 + 1 = 6
- Step 2: 6 + 3 = 9 (Note: 3 is 1 + 2)
- Step 3: 9 + 6 = 15 (Note: 6 is 1 + 2 + 3)
Following this pattern, the next number is found by adding 1 + 2 + 3 + 4 = 10 to the last number, 15.
Therefore:
- Step 4: 15 + 10 = 25
Calculation
Here's a table summarizing the pattern and the calculation:
| Series Number | Value | Calculation | Difference |
|---|---|---|---|
| 1 | 5 | Initial Value | |
| 2 | 6 | 5 + 1 | +1 |
| 3 | 9 | 6 + (1 + 2) | +3 |
| 4 | 15 | 9 + (1 + 2 + 3) | +6 |
| 5 | 25 | 15 + (1 + 2 + 3 + 4) | +10 |
Conclusion
Based on the pattern identified in the reference, where the amounts added increase by consecutive numbers (1, 3, 6, 10, etc.), the missing number is definitively 25. This pattern involves adding the sum of consecutive integers to the previous number in the series.
