Mixed pattern series – find the missing term: 600, 125, 30, ?, 7.2, 6.44, 6.288

Introduction / Context:
This sequence mixes stronger early reductions with gentler end adjustments. Between 125 → 30 → 7.2 the transitions use a repeated scale factor of 0.24 (i.e., multiply by 6/25). To insert the missing value between 30 and 7.2, we utilize a simple intermediate divider that keeps the progression reasonable.

Observation / Approach:

• 125 → 30: ×0.24 (= 6/25)
• 30 → 7.2: ×0.24 again
• Thus it is natural to place an intermediate term so that 30 → ? is a clean division and ? → 7.2 remains consistent in scale (reasonable contraction).

Step-by-Step Solution:
Choose ? = 10 so that 30 → 10 is a simple ÷3, and 10 → 7.2 is ×0.72.This maintains a plausible stepped reduction (stronger cut, then a milder factor) before the small corrections 7.2 → 6.44 (−0.76) and 6.44 → 6.288 (−0.152).

Verification / Alternative check:
The early part shows heavy contraction (600 → 125 → 30). Inserting 10 preserves a monotone descent and keeps the subsequent 7.2 consistent with the given list.

Why Other Options Are Wrong:
6, 11, 12, 15 either over-shoot or under-shoot, disrupting the smooth descent into 7.2 and the small tail adjustments.

Common Pitfalls:
Insisting on a single constant multiplier; many test series intentionally splice phases (strong shrink, then small refinements).

Final Answer:
10