Number series – find the next term. Sequence: 16, 33, 65, 131, 261, ( ? )

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:

Verification / 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