Series completion with alternating +30 and +60 increments: Fill the missing value that fits: 165, 195, 255, 285, ..., 435

Introduction / Context:
Observe alternating increments. When a series alternates between two fixed steps, apply them in turn to bridge from the start to the end.

Given Data / Assumptions:

• Partial series: 165, 195, 255, 285, ..., 435
• Differences: +30, +60, +30, ... (alternates +30 and +60)

Concept / Approach:
Continue the alternation: after +30 from 255 to 285, the next step is +60, followed by +30 to reach 435.

Step-by-Step Solution:
165 → 195 (+30)195 → 255 (+60)255 → 285 (+30)285 → 345 (+60)345 → 375 (+30), 375 → 435 (+60)

Verification / Alternative check:
Both end points are reached exactly when maintaining the +30, +60 alternating pattern.

Why Other Options Are Wrong:
340, 341, 401 break the alternation or misalign the final target 435.

Common Pitfalls:
Assuming a constant difference; the alternation is the key.

Final Answer:
345