Number series – find the next term. Sequence: 8, 7, 11, 12, 14, 17, 17, 22, ( ? )
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A27
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B20
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C22
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D24
Answer
Correct Answer: 20
Explanation
Introduction / Context:This sequence is formed by interleaving two simpler subsequences. Identifying and separating them is the key step to determining the next number.
Given Data / Assumptions:
- Main sequence: 8, 7, 11, 12, 14, 17, 17, 22, ( ? )
- Terms at odd positions and even positions likely follow different rules.
Concept / Approach:Extract the odd-position subsequence and the even-position subsequence. Analyze each for a consistent add pattern.
Step-by-Step Solution:
Odd positions (1,3,5,7): 8, 11, 14, 17 – this increases by +3 each time.Even positions (2,4,6,8): 7, 12, 17, 22 – this increases by +5 each time.The next term is the 9th (odd position), so apply the odd-position rule: 17 + 3 = 20.Verification / Alternative check:Project the even sequence further: after 22 would come 27, which matches option 27 but would be the 10th term, not the 9th. This cross-check supports 20 as the correct immediate next value.
Why Other Options Are Wrong:
- 27: Correct for the 10th term (even position), not for the 9th.
- 22 and 24: Do not match the +3 increment needed at odd positions after 17.
Common Pitfalls:Forcing a single rule on the entire list. Always consider interleaving when differences appear inconsistent.
Final Answer:20