In the letter triplet series ANT, CPV, ERX, ?, IVB, which triplet should replace the question mark to continue the pattern?

Introduction / Context:
Here you are given a series of three letter groups: ANT, CPV, ERX, ?, IVB. You must determine which triplet completes the pattern. Each position in the triplets first letter, second letter, and third letter follows its own arithmetic progression in alphabetical order, with wrap around for the third letters.

Given Data / Assumptions:

• Known triplets: ANT, CPV, ERX, ?, IVB.
• Alphabet positions A 1 to Z 26.
• We consider three separate sequences: first letters, second letters, third letters.
• Wrap around from Z back to A is allowed.

Concept / Approach:
We treat the first letters A, C, E, ?, I as one numeric series, the second letters N, P, R, ?, V as another, and the third letters T, V, X, ?, B as a third. For each column, we look for a constant difference. Once the pattern is clear, we extend each sequence by one step to obtain the missing triplet.

Step-by-Step Solution:
Step 1: First letters: A, C, E, ?, I. Step 2: Convert to numbers: A 1, C 3, E 5, I 9. Step 3: Differences from 1 to 3 to 5 are +2, +2. To reach I 9 from the missing term, we expect another +2. Step 4: So the missing first letter is 5 plus 2 equals 7, which is G. Then 7 plus 2 equals 9, matching I, so this is consistent. Step 5: Second letters: N, P, R, ?, V. Step 6: Positions: N 14, P 16, R 18, V 22. Step 7: Differences are +2, +2, and the jump from the missing term to V should again be +2. Step 8: So the missing second letter is 18 plus 2 equals 20, which is T. Step 9: Third letters: T, V, X, ?, B. Step 10: Positions: T 20, V 22, X 24, B 2. Step 11: We see +2 from 20 to 22, +2 from 22 to 24. Another +2 from the missing letter should then lead to B 2, using wrap around. Step 12: Let the missing third letter have position k. Then k plus 2 modulo 26 equals 2. So k must be 26, which is Z. Step 13: Therefore, the missing triplet is GTZ.

Verification / Alternative check:
Write the full pattern including GTZ: ANT, CPV, ERX, GTZ, IVB. First letters are A, C, E, G, I (1,3,5,7,9) with consistent step +2. Second letters are N, P, R, T, V (14,16,18,20,22) with step +2. Third letters are T, V, X, Z, B (20,22,24,26,2) with step +2 and correct wrap around at Z. No other candidate triplet produces such neat patterns in all three columns.

Why Other Options Are Wrong:
FSY and FSZ have wrong first and second letters because they do not match the +2 progressions. GTY has the first two letters correct but uses Y instead of Z, which breaks the +2 wrap around logic for the third letters. Therefore only GTZ satisfies the pattern for all three positions.

Common Pitfalls:
Sometimes learners only look at the first letters and ignore the second and third columns, which can lead to partially correct guesses. Another common error is not allowing wrap around from Z to A when dealing with fixed steps. Always check each column separately and confirm that your candidate works for all letter positions simultaneously.

Final Answer:
The triplet that correctly completes the series is GTZ.