Odd term in an “add 1,2,3,4 then 5,6,7,8 …” ladder: 4, 5, 7, 10, 14, 18, 25, 32

Introduction / Context:This series uses a growing ladder of consecutive additions grouped in runs: +1, +2, +3, +4, then +5, +6, +7, +8, and so on. A single term undercuts the expected addition, revealing itself as the odd one out.

Given Data / Assumptions:

• Sequence: 4, 5, 7, 10, 14, 18, 25, 32.
• Hypothesized additions: +1, +2, +3, +4, +5, +6, +7, +8.

Concept / Approach:Compute successive differences and match them against the intended ladder. The incorrect step will be short by the expected increment.

Step-by-Step Solution:5 − 4 = +17 − 5 = +210 − 7 = +314 − 10 = +418 − 14 = +4 (should be +5) ✗25 − 18 = +7 (as if the ladder resumed later)32 − 25 = +7 (should be +8 if continuing strictly)

Verification / Alternative check:If 18 were 19 (adding +5 correctly), the next should be +6 to 25, then +7 to 32, and +8 would follow. The earliest break is at 18, making it the odd term.

Why Other Options Are Wrong:

• 7 / 14 / 32 fit or are reconcilable once the +5 step is restored; 18 uniquely under-delivers by 1.

Common Pitfalls:

• Overlooking grouped runs of consecutive additions; ensuring the ladder increments correctly pinpoints the anomaly.

Final Answer:18