Wrong Term in the Cubic-Difference Series: 2, 3, 11, 38, 102, 229, 443 — one term breaks the pattern where successive differences should be 1^3, 2^3, 3^3, 4^3, 5^3, 6^3.

Introduction / Context:
Progressive-difference series often use perfect powers as successive increments. Here the intended differences are consecutive cubes.

Given Data / Assumptions:

• Proposed rule: a(n) = a(n-1) + k^3 for k = 1, 2, 3, 4, 5, 6, …
• Starting from 2, the correct cumulative path should be +1, +8, +27, +64, +125, +216, …

Concept / Approach:
Compute actual differences and compare to the target k^3 milestones.

Step-by-Step Solution:
2 → 3: +1 = 1^3 ✓3 → 11: +8 = 2^3 ✓11 → 38: +27 = 3^3 ✓38 → 102: +64 = 4^3 ✓102 → 229: +127 (should be +125 = 5^3) ✗If corrected to 102 + 125 = 227, then 227 → 443 would be +216 = 6^3 ✓

Verification / Alternative check:
Every step aligns with perfect cubes if 229 is replaced by 227; no other single-term change achieves perfect alignment.

Why Other Options Are Wrong:

• 11, 38, 102, 443: each sits exactly at the cumulative totals expected from the +1, +8, +27, +64, +216 scheme (with the 5th increment corrected to 125).

Common Pitfalls:
Mistaking 127 for 125 (5^3). This small slip is a classic trap in cube-based difference series.

Final Answer:
229