Find the missing term in the given series: 25, ?, 36, 43, 64, 73, 121.

Concept: An alternating (interleaved) number series is built from two independent sub-series occupying alternating positions — the 1st, 3rd, 5th, 7th terms follow one rule, and the 2nd, 4th, 6th terms follow a different rule that reuses the same base values as the odd-position rule. To find a missing term, separate the two sets of positions, discover each sub-series' own rule, then apply the matching rule to the missing position.

Application: Applying this to the series 25, ?, 36, 43, 64, 73, 121:

1. The odd-position terms (1st, 3rd, 5th, 7th) are 25, 36, 64, 121 — the squares of 5, 6, 8, 11, where the bases increase by 1, then 2, then 3.

2. The even-position terms (2nd, 4th, 6th) are ?, 43, 73 — each one is generated from the same base as the odd-position term immediately before it.

3. Checking the rule on the two even-position terms that are already known: from base 6, 62 + 7 = 43; from base 8, 82 + 9 = 73 — in both cases the rule is base2 + (base + 1).

4. Applying the same rule to the missing 2nd term, whose base is 5 (since 52 = 25): 52 + (5 + 1) = 25 + 6 = 31.

Cross-check: The rule base2 + (base + 1) holds for every even-position term that is already given — 62 + 7 = 43 and 82 + 9 = 73 both match — and the odd-position bases 5, 6, 8, 11 (increasing by 1, 2, 3) also hold without exception. Both checks confirm the missing term.

Result: The missing term is 31.