Find the incorrect term in the following number series. Series: 1, 3, 10, 21, 64, 129, 356, 777

Introduction / Context:
This numeric reasoning task asks you to detect which term does not fit a hidden rule. Many exam series interleave two simpler subseries (odd and even positions). If each subseries follows a clean rule, any violation reveals the incorrect term.

Given Data / Assumptions:

• Series: 1, 3, 10, 21, 64, 129, 356, 777
• We test separation into odd-position and even-position strands.
• We look for a consistent linear recurrence of the form next = 6current + c.

Concept / Approach:
Split the list: odd positions → 1, 10, 64, 356; even positions → 3, 21, 129, 777. Check each strand for a simple multiplier-plus-constant rule. If one value breaks the pattern, that value is the wrong term.

Step-by-Step Solution:
Even-position strand: 3 → 21 → 129 → 777 follows next = 6current + 3 (since 63+3=21; 621+3=129; 6129+3=777). Odd-position strand: 1 → 10 → 64 should follow the analogous rule next = 6current + 4 (61+4=10; 610+4=64). Applying that rule again: 6*64 + 4 = 384 + 4 = 388. The series shows 356 instead of 388. Therefore 356 violates the governing rule.

Verification / Alternative check:
Replacing 356 with 388 yields two perfectly consistent strands with the same structure constants (+3 for even strand, +4 for odd strand).

Why Other Options Are Wrong:
21, 129, 10 all satisfy their respective strand rules; removing any of them would break a consistent recurrence.

Common Pitfalls:
Trying to fit one global rule to all terms, instead of separating the interleaved subsequences.

Final Answer:
356