Number series (find the wrong term): 1, 3, 10, 21, 64, 129, 356, 777 Find the single term that breaks the alternating multiplication pattern and justify your answer.

Introduction / Context:
Alternating operations (e.g., multiply by 2 then by 3) are very common in series. This sequence strongly suggests a “multiply and add” alternation with a small constant. We will test a repeating two-step rule.

Given Data / Assumptions:

• Series: 1, 3, 10, 21, 64, 129, 356, 777
• Exactly one term is wrong.

Concept / Approach:
Look for an alternating pattern: 2 + 1, then 3 + 1, repeating. Verify across the sequence.

Step-by-Step Solution:
1 → 3: 12 + 1 = 3 ✔3 → 10: 33 + 1 = 10 ✔10 → 21: 102 + 1 = 21 ✔21 → 64: 213 + 1 = 64 ✔64 → 129: 642 + 1 = 129 ✔Next should be 1293 + 1 = 388, but the series lists 356 ✖Continuing the rule from the corrected value: 388*2 + 1 = 777, which matches the final term ✔

Verification / Alternative check:
With 356 corrected to 388, every transition satisfies the alternating pattern (*2 + 1, *3 + 1), and the last term remains consistent.

Why Other Options Are Wrong:

• 10, 21, 64, 129: Each perfectly fits the alternating rule.
• 356: The only value that breaks the rule; it should be 388.

Common Pitfalls:
Trying only constant differences or ratios; alternating mixed operations are frequently used to disguise a simple rule.

Final Answer:
356