The next number in the series 2, 5, 10 is 17.
Understanding the Pattern
The given sequence is not an arithmetic progression (where the difference between consecutive terms is constant) or a geometric progression (where the ratio between consecutive terms is constant). Instead, it follows a pattern based on increasing the difference between consecutive terms.
Detailed Analysis:
- The difference between 5 and 2 is 3 (5-2 = 3).
- The difference between 10 and 5 is 5 (10-5 = 5).
Notice that the differences (3 and 5) are consecutive odd numbers. Based on the reference, which indicates the common difference is the next odd number, the next difference should be 7. Therefore, the next number in the sequence can be calculated as follows:
- 10 + 7 = 17
Full Series:
Based on the reference, the series is 2, 5, 10, 17, 26, 37... Let's break down the differences:
| Sequence | Difference |
|---|---|
| 2 | |
| 5 | 3 |
| 10 | 5 |
| 17 | 7 |
| 26 | 9 |
| 37 | 11 |
As you can see, the differences (3, 5, 7, 9, 11...) form an increasing sequence of consecutive odd numbers.
Conclusion
Therefore, the next number in the sequence 2, 5, 10 is 17. The sequence continues as 2, 5, 10, 17, 26, 37, and each consecutive number is obtained by adding the next odd number to the previous number.
