Look at this series: VI, 10, V, 11, __, 12, III, ... Which term completes the…

An alternating (interleaved) number series merges two independent subsequences into a single list, taking terms from each subsequence by turn. To solve such a series, separate the terms by their position into the two subsequences and find the rule governing each independently.

1. Split the given series by position: the 1st, 3rd, 5th, 7th terms form one subsequence, and the 2nd, 4th, 6th terms form the other.

2. 1st, 3rd, 5th, 7th terms: VI, V, __, III — in numeric value this reads 6, 5, __, 3.

3. 2nd, 4th, 6th terms: 10, 11, 12 — each increases by 1, confirming this subsequence's rule.

4. Applying the same logic to the other subsequence: 6, 5, __, 3 decreases by 1 at each step, so the missing value is 5 − 1 = 4, written as the Roman numeral IV.

Cross-check: continuing the decreasing-by-1 rule from 4 gives 4 − 1 = 3, which matches the next given term (III) in the series, confirming the pattern holds throughout.

So the blank is filled by IV.