Difficulty: Easy
Correct Answer: 27
Explanation:
Introduction / Context:This is a classic “Mersenne-like” sequence test where terms are one less than powers of 2. One value does not fit that model.
Given Data / Assumptions:
Concept / Approach:
Compute 2^n - 1 for n = 2, 3, 4, 5, 6, 7, 8 to see what the sequence should be.
Step-by-Step Solution:
2^2 - 1 = 3 ✓2^3 - 1 = 7 ✓2^4 - 1 = 15 ✓2^5 - 1 = 31 (but the series shows 27) ✗2^6 - 1 = 63 ✓2^7 - 1 = 127 ✓2^8 - 1 = 255 ✓Verification / Alternative check:
Replacing 27 with 31 restores the exact 2^n - 1 progression across all terms.
Why Other Options Are Wrong:
7, 15, 63, 127 match perfect Mersenne form with their respective exponents and are correct.
Common Pitfalls:
Looking for differences obscures the simpler power-of-two relationship.
Final Answer:
27
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