The next number in the series 5, 16, 49, 104 is 181, according to the provided reference.
Analysis of the Series
While the reference directly provides the answer, let's examine a possible pattern to understand how it might have been derived. Identifying the underlying pattern helps confirm the solution.
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Differences between terms: We can look at the differences between consecutive numbers to see if there's a discernible progression.
- 16 - 5 = 11
- 49 - 16 = 33
- 104 - 49 = 55
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Differences between the differences: The differences (11, 33, 55) themselves form a pattern.
- 33 - 11 = 22
- 55 - 33 = 22
Since the second differences are constant (22), we can assume a quadratic relationship governs the sequence. We can project that the next difference between terms should be 55 + 22 = 77. Therefore, the next number in the series would be 104 + 77 = 181.
Verification
This analysis supports the answer of 181 found in the reference material.
