Number series (find the wrong term): 3, 7, 15, 39, 63, 127, 255, 511 Determine the one term that does not belong to the underlying rule and explain why.

Introduction / Context:
This sequence strongly suggests the form 2^n − 1 (Mersenne-type numbers). We will verify each term against this rule and isolate the misfit.

Given Data / Assumptions:

• Series: 3, 7, 15, 39, 63, 127, 255, 511
• Exactly one number is wrong.

Concept / Approach:
Compute 2^n − 1 for successive n: 2^2 − 1 = 3, 2^3 − 1 = 7, 2^4 − 1 = 15, 2^5 − 1 = 31, 2^6 − 1 = 63, 2^7 − 1 = 127, 2^8 − 1 = 255, 2^9 − 1 = 511.

Step-by-Step Solution:
3 ✔7 ✔15 ✔Next should be 31, but the series lists 39 ✖Then 63 ✔, 127 ✔, 255 ✔, 511 ✔

Verification / Alternative check:
Replace 39 with 31 and the entire sequence becomes consecutive 2^n − 1 values for n = 2 through 9.

Why Other Options Are Wrong:

• 7, 15, 63, 127: All equal 2^n − 1 for some n.
• 39: Not equal to 2^n − 1 for any integer n; thus it is the misfit.

Common Pitfalls:
Confusing powers of 2 minus 1 with nearby values (e.g., 31 vs. 39). Always verify by quick powers: 16, 32, 64, …

Final Answer:
39