Number series – find the next term. Sequence: 16, 33, 65, 131, 261, ( ? )
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A523
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B521
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C613
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D721
Answer
Correct Answer: 523
Explanation
Introduction / Context:Next-term series often alternate between two closely related operations. Recognizing the alternation is key to predicting the following number with confidence.
Given Data / Assumptions:
- Sequence terms: 16, 33, 65, 131, 261
- We need the next term.
Concept / Approach:Test a pattern of doubling with small adjustments. A classic alternation is multiply by 2 then add 1, followed by multiply by 2 then subtract 1, repeating.
Step-by-Step Solution:
16 * 2 + 1 = 3333 * 2 − 1 = 6565 * 2 + 1 = 131131 * 2 − 1 = 261Next continues the alternation: 261 * 2 + 1 = 523Verification / Alternative check:Check parity: the +1 steps produce odd numbers, and the −1 steps also produce odd numbers, consistent with all terms being odd except the first. The alternating adjustments confirm the rule.
Why Other Options Are Wrong:
- 521, 613, 721: These do not follow the multiply by 2 with alternating ±1 rule from the previous term 261.
Common Pitfalls:Trying constant differences or ratios. The near doubling suggests testing a slight alternating offset from exact 2x.
Final Answer:523