Wrong Term at the Tail of a Fibonacci-like Increment Series: 2, 3, 5, 8, 14, 23, 41, 69 — find the lone wrong term by analyzing the intended pattern of cumulative increments.

Introduction / Context:
Several series use increasing differences that themselves follow a simple additive pattern. A single miscopy at the end often breaks a near-Fibonacci run of differences.

Given Data / Assumptions:

• Series: 2, 3, 5, 8, 14, 23, 41, 69.
• Observed differences: +1, +2, +3, +6, +9, +18, +28.

Concept / Approach:
Notice that the differences roughly follow a rule of “add the previous significant jump” (3, then 6 = 3+3, then 9 = 3+6, then 18 = 9+9). By that logic, after +18, the next should be +27 (not +28).

Step-by-Step Solution:
2 → 3: +13 → 5: +25 → 8: +38 → 14: +6 (≈ 3 + 3)14 → 23: +9 (≈ 3 + 6)23 → 41: +18 (≈ 9 + 9)Next expected jump: 27 (≈ 9 + 18), hence 41 + 27 = 68; but the series shows 69.

Verification / Alternative check:
With 68 in place of 69, the increments form a consistent internal pattern without forcing earlier edits.

Why Other Options Are Wrong:

• 8, 14, 23, 41: each fits the derived increment logic; only the final term overshoots by 1.

Common Pitfalls:
Trying to retrofit a multiplicative rule; the additive increment structure is the minimal-consistency explanation.

Final Answer:
69