Number series – multiply by 1.5, 2, 2.5, 3, 3.5, 4, ... (factors rise by 0.5): 16, 24, 48, 120, 360, 1260, ? Continue the half-step growth in multipliers.

Introduction / Context:Here the sequence grows via changing multiplicative factors that increase by 0.5 each time: ×1.5, ×2.0, ×2.5, ×3.0, ×3.5, and so on. Such “laddered multipliers” are a frequent pattern.

Given Data / Assumptions:

• 16 → 24 (×1.5)
• 24 → 48 (×2.0)
• 48 → 120 (×2.5)
• 120 → 360 (×3.0)
• 360 → 1260 (×3.5)

Concept / Approach:The next multiplier is ×4.0. Apply it to 1260.

Step-by-Step Solution:

Verification / Alternative check:Sequence of multipliers (1.5, 2.0, 2.5, 3.0, 3.5, 4.0) is perfectly regular.

Why Other Options Are Wrong:

Common Pitfalls:Mistaking these for factorial products; while 5040 equals 7!, the generative rule here is the multiplier ladder.

Final Answer:5040