Complete the mixed-step series: 45, 54, 47, ?, 49, 56, 51, 57, 53 — identify the alternating increase/decrease pattern to find the missing term.

Introduction / Context:This series alternates between increases and decreases with changing step sizes. Recognizing the two interleaved operations (add, then subtract) with a controlled change in the step values is key.

Given Data / Assumptions:

• Series: 45, 54, 47, ?, 49, 56, 51, 57, 53.
• Observed alternating pattern: + then − then + then − …

Concept / Approach:Write consecutive differences and look for a secondary pattern in the step sizes. In many puzzles, the “add” steps decrease gradually, while the “subtract” steps also change by a fixed rule.

Step-by-Step Solution:

Verification / Alternative check:The symmetric step reductions (+9, +8, +7, +6 … and −7, −6, −5, −4 …) remain consistent across the entire sequence.

Why Other Options Are Wrong:

• 48 or 50 would break the required next difference of +8 and derail subsequent terms.
• “None of these” is invalid because 55 cleanly preserves the pattern.

Common Pitfalls:Treating the series as one uniform arithmetic progression rather than alternating add/subtract with gradually changing step sizes.

Final Answer:55