Odd One Out — For the quartets (11, 17, 23), (12, 14, 16), (8, 10, 12), (18, 36, 72), three are arithmetic progressions; one is a geometric progression. Identify it.

Introduction / Context:Sequence classification frequently contrasts arithmetic progression (AP) with geometric progression (GP). We locate the single GP among three APs.

Given Data / Assumptions:

• AP: constant difference between consecutive terms.
• GP: constant ratio between consecutive terms.

Concept / Approach:Compute differences and ratios for each sequence and classify accordingly.

Step-by-Step Solution:(11, 17, 23): differences +6 and +6 → AP.(12, 14, 16): differences +2 and +2 → AP.(8, 10, 12): differences +2 and +2 → AP.(18, 36, 72): ratios ×2 and ×2 → GP.

Verification / Alternative check:No uniform difference fits (18, 36, 72); no uniform ratio fits the other three. This cleanly separates one GP from the APs.

Why Other Options Are Wrong:

• (11, 17, 23): AP.
• (12, 14, 16): AP.
• (8, 10, 12): AP.

Common Pitfalls:Mistaking “even-only” as a defining feature; parity does not determine AP vs GP.

Final Answer:18, 36, 72