Understanding the Sequence
To find the missing value in the sequence 2, 5, 9, 14, _, 27, we first need to analyze the differences between consecutive numbers.
Finding Differences
- The difference between 2 and 5 is:
- 5 - 2 = 3
- The difference between 5 and 9 is:
- 9 - 5 = 4
- The difference between 9 and 14 is:
- 14 - 9 = 5
- The difference between 14 and the missing number (let's call it x):
- The difference between x and 27 is:
- 27 - x
Identifying a Pattern
The differences observed are as follows:
- First difference: 3
- Second difference: 4
- Third difference: 5
This suggests a pattern where the differences increase by 1 each time. Continuing this pattern:
- The next difference (from 14 to x) should be 6.
- The difference from x to 27 should be 7.
Calculating the Missing Value
1. From 14 to x:
- x = 14 + 6 = 20
2. From x to 27:
- 27 - 20 = 7 (which confirms our pattern)
Conclusion
Thus, the missing value in the sequence is:
- 20
The complete sequence is 2, 5, 9, 14, 20, 27. This systematic approach of identifying differences helps in determining the missing elements in numerical sequences effectively.