A sequence of three letter groups is given with one term missing. Choose the group that correctly completes the pattern: BFK, KOT, UYD, ?

Introduction / Context:
This is an alphabet series problem where each term is a three letter group, and the pattern involves increasing step sizes in letter positions. You need to detect how each letter in the triplets moves and then predict the next group. Recognizing varying step increments is crucial for solving such questions accurately.

Given Data / Assumptions:

• Given groups: BFK, KOT, UYD, ? • Alphabet positions: A = 1 to Z = 26. • First, second, and third letters each follow their own numeric sequence. • The increment between terms can change but should do so in a simple pattern.

Concept / Approach:
We separately analyze the first letters (B, K, U), the second letters (F, O, Y), and the third letters (K, T, D). We convert each to numeric form and check the differences: if we see steps like +9, +10, etc., we can extend the pattern logically. Once we identify the next position values, we convert them back to letters to form the missing group.

Step-by-Step Solution:
Step 1: Analyze the first letters: B, K, U. Positions: B = 2, K = 11, U = 21. Differences: 2 → 11 is +9, 11 → 21 is +10. The increment increases by 1, so the next step should be +11. Next first letter: 21 + 11 = 32, 32 − 26 = 6, which is F. Step 2: Analyze the second letters: F, O, Y. Positions: F = 6, O = 15, Y = 25. Differences: 6 → 15 is +9, 15 → 25 is +10. Again, the increment rises by 1, so the next step is +11. Next second letter: 25 + 11 = 36, 36 − 26 = 10, which is J. Step 3: Analyze the third letters: K, T, D. Positions: K = 11, T = 20, D = 4. Differences: 11 → 20 is +9, 20 → 4 corresponds to +10 modulo 26 (20 + 10 = 30, 30 − 26 = 4). So the next difference is +11. Next third letter: 4 + 11 = 15, which is O. Step 4: Combine letters to get the missing term FJO.

Verification / Alternative check:
We can summarize the numeric sequences: first letters 2, 11, 21, 6 (with +9, +10, +11), second letters 6, 15, 25, 10, and third letters 11, 20, 4, 15, all using the same +9, +10, +11 pattern under modulo 26. This consistent structure confirms FJO as the correct continuation.

Why Other Options Are Wrong:
• BFJ: This breaks the growing step pattern in all three letter positions. • ADG: These letters do not match the predicted numeric results after applying the +11 increment from the previous term. • PSX: While visually similar in length, this option fails to satisfy the arithmetic relationships for any of the letter columns.

Common Pitfalls:
Some test takers only look at letter shapes or approximate distances rather than exact numeric increments, leading them away from the consistent +9, +10, +11 pattern. Others may forget to handle wrap around when values exceed 26. Using explicit modular arithmetic helps avoid such errors.

Final Answer:
The three letter group that correctly completes the series is FJO.