Number series — find the next two terms of the sequence (alternating +3 and −1): 9, 12, 11, 14, 13, 16, 15
Verbal Reasoning
Number Series
Difficulty: Easy
Choose an option
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A14 13
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B18 21
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C14 17
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D12 13
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E18 17
Answer
Correct Answer: 18 17
Explanation
Introduction / Context:Alternating-operation sequences apply two different steps in turn, such as “add A, subtract B, add A, subtract B…”. Detecting this alternation enables rapid extension of the sequence to future terms without confusion.
Given Data / Assumptions:
- Sequence: 9, 12, 11, 14, 13, 16, 15
- We need positions 8 and 9.
- Visual inspection suggests alternating +3 and −1.
Concept / Approach:Confirm the alternating pattern by calculating consecutive differences. Then apply the same two-step cycle to the last known term to compute the next two values precisely.
Step-by-Step Solution:
Differences: +3 (9→12), −1 (12→11), +3 (11→14), −1 (14→13), +3 (13→16), −1 (16→15).Continue alternation: next is +3 → 15 + 3 = 18.Then −1 → 18 − 1 = 17.Therefore, the next two terms are 18 and 17.Verification / Alternative check:
Apply the same rule earlier: 11 + 3 = 14, 14 − 1 = 13; it holds throughout, validating the alternation.Why Other Options Are Wrong:
14 13 / 12 13 / 14 17 / 18 21: Each pair violates the strict +3 then −1 alternation at one or both steps.Common Pitfalls:
Replacing the alternating pattern with a single AP; overlooking the small −1 steps between +3 jumps.Final Answer:18 17