In the series below, you will be looking at both the letter pattern and the…

Concept: In a compound letter-and-number series, each term is built from independent sub-sequences layered together — for instance, one letter position may follow its own alphabetical rule, a second letter position may follow a different alphabetical rule, and an embedded number may follow its own arithmetic rule, including which position within the term it occupies. Solve such a series by isolating and tracking each sub-sequence separately, then recombining them for the missing term.

Application:

1. First letter of each term: Z, Y, X, W — each step moves one letter backward through the alphabet, so the next first letter is V.

2. Second letter of each term: A, B, C, D — each step moves one letter forward through the alphabet, so the next second letter is E.

3. Embedded number: 5, 4, 6, 3 — the differences between consecutive numbers are −1, +2, −3 (the step size grows by one each time and the sign alternates), so the next difference is +4, giving 3 + 4 = 7.

4. Position of the number within the term: after both letters in the 1st term, between the two letters in the 2nd term, after both letters in the 3rd term, between the two letters in the 4th term — the position alternates every step, so the 5th term places the number after both letters, at the end, matching the 1st and 3rd terms.

Cross-check: Reapplying all three sub-sequence rules together — the backward-letter rule, the forward-letter rule, and the alternating-difference rule, positioned per the same alternation as the 1st and 3rd terms — reproduces a term with the same overall shape as those two terms, confirming the derivation is internally consistent.

Result: the missing term is VE7, at the end.