Odd One Out — Among 2–4–8, 4–16–32, 3–9–27, 5–25–125, select the only triplet that is not (n, n^2, n^3).

Introduction / Context:Power progressions are a classic theme: many triplets take the form (n, n^2, n^3). We identify the single triplet that does not fit.

Given Data / Assumptions:

• 2–4–8 → 2, 2^2, 2^3.
• 3–9–27 → 3, 3^2, 3^3.
• 5–25–125 → 5, 5^2, 5^3.
• 4–16–32 → 4, 4^2, but 4^3 = 64 (not 32).

Concept / Approach:Compute squares and cubes of the first element and compare with the second and third elements of each triplet.

Step-by-Step Solution:2^2 = 4, 2^3 = 8 → matches.3^2 = 9, 3^3 = 27 → matches.5^2 = 25, 5^3 = 125 → matches.4^2 = 16, 4^3 = 64 → third is 32 ✗

Verification / Alternative check:Check ratios: in a true (n, n^2, n^3), ratios are n and n; only the 4-based triplet shows 16/4 = 4 and 32/16 = 2, not equal.

Why Other Options Are Wrong:

• 2–4–8: valid power triplet.
• 3–9–27: valid power triplet.
• 5–25–125: valid power triplet.

Common Pitfalls:Assuming geometric progression suffices. A GP with ratio 2 can also appear, but (n, n^2, n^3) imposes equal successive ratios (both equal to n).

Final Answer:4-16-32