Number series (three interleaved arithmetic threads, step ±6) Sequence: 4 7 26 10 13 20 16 … Choose the next two numbers.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Some sequences are formed by interleaving multiple simpler arithmetic threads. Here, terms at positions 1, 4, 7; 2, 5, 8; and 3, 6, 9 each follow their own linear rule. Given Data / Assumptions: Total sequence shown: 4, 7, 26, 10, 13, 20, 16, … Consider three position-based subsequences: (1,4,7,…), (2,5,8,…), (3,6,9,…). Concept / Approach:Extract and analyze each thread separately. If each progresses by ±6, you can predict the next corresponding values, then interleave back. Step-by-Step Solution: Thread A (positions 1,4,7,…): 4 → 10 → 16 (adds +6 each time). Next value = 16 + 6 = 22 (used at position 10; note we still need positions 8 and 9 first).Thread B (positions 2,5,8,…): 7 → 13 → next = 13 + 6 = 19 (this is position 8, the next term after 16).Thread C (positions 3,6,9,…): 26 → 20 → next = 20 − 6 = 14 (this is position 9, the second term required).Therefore, the next two numbers (positions 8 and 9) are 19 and 14. Verification / Alternative check:Continuing, position 10 (thread A) would be 22, maintaining the ±6 pattern across the three threads. Why Other Options Are Wrong: 14 4 / 14 17 / 18 14 / 19 13: Each breaks at least one thread’s ±6 rule or mis-orders the interleaving. Common Pitfalls:Analyzing only one difference stream instead of separating by positions. Final Answer:19 14

Number series (three interleaved arithmetic threads, step ±6) Sequence: 4 7 26 10 13 20 16 … Choose the next two numbers.

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