The next term in the series −1, 5, 15, 29, ?, ... is:
47
To find the pattern and determine the next term in the series: -1, 5, 15, 29, ?, we need to analyze the differences between consecutive terms.
- First, calculate the difference between each consecutive term in the series:
- Difference between the 2nd term (5) and the 1st term (-1) is: \(5 - (-1) = 6\)
- Difference between the 3rd term (15) and the 2nd term (5) is: \(15 - 5 = 10\)
- Difference between the 4th term (29) and the 3rd term (15) is: \(29 - 15 = 14\)
- Observe the pattern in the differences: 6, 10, 14.
- Notice that these differences increase by 4 with each consecutive term:
- First difference: 6
- Second difference: 10 (\(6 + 4\))
- Third difference: 14 (\(10 + 4\))
- Following this pattern, the next difference should be:
- Fourth difference: \(14 + 4 = 18\)
- Add this difference to the last known term in the series:
- The next term is: \(29 + 18 = 47\)
Therefore, the next term in the series is 47.
This pattern of consecutive differences increasing consistently helps in predicting the next term accurately.
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