A three letter alphabet series is given with one term missing: TUW, ZAC, FGI, LMO, ?. Which group of three letters should replace the question mark so that the pattern of the series is preserved?

Introduction / Context:
This problem tests pattern recognition in a sequence of three letter groups. The given sequence is TUW, ZAC, FGI, LMO, ?, and the task is to find which group of three letters completes the series logically. These kinds of alphabet series questions are very common in competitive examinations and evaluate a candidate ability to detect regular increments and cyclic movement in the English alphabet.

Given Data / Assumptions:

• Given terms: TUW, ZAC, FGI, LMO, and one missing term.
• Each term contains three capital letters.
• The pattern, if present, should apply consistently to all three positions in each group.
• We consider wrap around from Z back to A when necessary.
• Answer options: PQS, RSU, QRT, UVX.

Concept / Approach:
The main idea is to convert each letter into its position number in the alphabet and then look for a consistent step size. If the same addition is applied in a cycle to the first, second, and third letters separately, then we can extend the pattern to the next term. This method makes hidden patterns much more obvious, especially when the alphabet wraps around after Z.

Step-by-Step Solution:
Step 1: Convert letters to positions. T, U, W correspond to 20, 21, 23. Z, A, C correspond to 26, 1, 3. F, G, I correspond to 6, 7, 9. L, M, O correspond to 12, 13, 15.Step 2: Focus on the first letters of each term: T(20), Z(26), F(6), L(12). The steps are +6 (20 to 26), then +6 with wrap around (26 to 6), and again +6 (6 to 12).Step 3: Continue this pattern by adding +6 once more to 12. We get 12 + 6 = 18, which is the letter R.Step 4: Repeat the same check for the second letters: U(21), A(1), G(7), M(13). The movement is +6 each time with wrap around, so from 13 plus 6 gives 19, which is S.Step 5: Now check the third letters: W(23), C(3), I(9), O(15). Again the step size is +6, so from 15 we get 21, which corresponds to U.Step 6: Therefore the next term must be RSU, matching the position pattern for all three letters.

Verification / Alternative check:
We can verify by reconstructing the entire pattern: TUW (20, 21, 23) then adding 6 repeatedly to each position gives ZAC (26, 1, 3), then FGI (6, 7, 9), then LMO (12, 13, 15), and finally RSU (18, 19, 21). The pattern of a constant +6 step is consistent. No other option fits all three letter positions with a uniform step of +6, so RSU is uniquely correct.

Why Other Options Are Wrong:
PQS, QRT, and UVX do not follow the exact +6 step for all three letter positions when placed after LMO. They would break the uniform transformation rule that we identified. Since the sequence is based on a consistent mathematical pattern, any option that violates this rule must be rejected.

Common Pitfalls:
Many learners look only at the surface appearance of letters and do not check each position separately. Others may try to guess based on visual similarity instead of computing letter positions. Converting letters to numbers and checking each sequence (first, second, and third letters) avoids these issues and leads to a systematic solution.

Final Answer:
The correct group of letters that completes the series is RSU.