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Number series — find the next two terms of the sequence (alternating +3 and −1): 9, 12, 11, 14, 13, 16, 15

Difficulty: Easy

14 13
18 21
14 17
12 13
18 17

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.

Number series — find the next two terms of the sequence (alternating +3 and −1): 9, 12, 11, 14, 13, 16, 15

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