Number series — continue the pattern. Sequence: 1, 2, 6, 7, 21, 22, 66, 67, ?

Introduction / Context: This sequence alternates between multiplying by 3 and then adding 1. Such two-step cycles are common in reasoning tests. Recognizing the cycle allows you to project the next value confidently.

Given Data / Assumptions:

• Sequence chunks appear as pairs: (1, 2), (6, 7), (21, 22), (66, 67)...
• Within each pair, the first number seems to be tripled from a previous term, and the second number is that result plus 1.
• We extend the same two-step rule forward.

Concept / Approach: Identify the repeating cycle: ×3, then +1. Apply it from the last two numbers to determine the next.

Step-by-Step Solution: From 66 to 67 is +1, completing a pair. The next step starts a new pair by applying ×3 to 67: 67 × 3 = 201. Thus the next term (the first of the new pair) is 201.

Verification / Alternative check: Check earlier transitions: 2 → 6 (×3), 6 → 7 (+1); 7 → 21 (×3), 21 → 22 (+1); 22 → 66 (×3), 66 → 67 (+1). Pattern is consistent.

Why Other Options Are Wrong: 70/134/301: Do not equal 67 × 3. They would break the ×3, +1 alternation that fits every prior pair.

Common Pitfalls: Applying +1 again after 67, forgetting the cycle restarts with ×3.

Final Answer: 201