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Question

Difficulty: MediumNumber and Alphabet Series
Determine the next term that logically completes the following numerical sequence:
4,7,14,27,48,79,…4, 7, 14, 27, 48, 79, \dots

Answer: 122

Answer

The next term in the sequence is 122.
The sequence follows a double-difference pattern. The differences between successive terms are 3, 7, 13, 21, 31. Taking the differences of these values gives 4, 6, 8, 10, which increases by 2 each time. The next second-order difference must be 12, making the next first-order difference 31 + 12 = 43. Adding 43 to 79 gives the final result of 122.

Step-by-Step Solution

1
Calculate the first-order differences between consecutive terms
The first differences are 3, 7, 13, 21, and 31.
Identifying the rate of increase helps determine the underlying rule.
2
Calculate the second-order differences
The second differences are 4, 6, 8, and 10.
Since the first differences are not constant, analyzing second-level differences reveals higher-order patterns.
3
Extend the second-difference pattern to find the next first difference and term
Next second difference = 12, next first difference = 43, next term = 79 + 43 = 122.
The second differences form an arithmetic sequence adding 2 at each step.

Key Concept

Double-Difference Numerical Series
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Topics

Number and Alphabet Series

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