Set pattern matching: “Given set: (15, 27, 39)” — choose the option whose three numbers follow the same pattern (constant common difference).

Introduction / Context:The given set (15, 27, 39) forms an arithmetic progression with common difference 12. We need a choice set that also exhibits a constant common difference (not necessarily the same value), preserving the “AP structure.”

Given Data / Assumptions:

• (15, 27, 39) differences: +12, +12.

Concept / Approach:Scan options for a trio with identical successive differences.

Step-by-Step Solution:1) (105, 125, 145): +20, +20 → constant difference.2) Other options either mix values or fail to maintain equal gaps.

Verification / Alternative check:Arithmetic progressions require d(n+1 − n) to be equal for each step; only option (105, 125, 145) satisfies this strictly.

Why Other Options Are Wrong:They lack a consistent common difference across both gaps.

Common Pitfalls:Choosing sets that look “roughly increasing” but are not true APs.

Final Answer:(105, 125, 145)