Letter series puzzle: In the sequence A, F, Z, U, G, L, T, what is the next letter that should come after T?

Introduction / Context:
This question presents a letter series puzzle: A, F, Z, U, G, L, T, ?. The task is to determine which letter should correctly continue the pattern. Such puzzles test a student's ability to recognize hidden structures in sequences, particularly patterns involving positions of letters in the English alphabet and how those positions change from term to term. Understanding this kind of reasoning is important in competitive exams and logical reasoning sections.

Given Data / Assumptions:
- The given sequence is: A, F, Z, U, G, L, T, followed by a missing letter.
- Only one of the options K, M, O, or Q continues the sequence correctly.
- The English alphabet positions are assumed as A = 1, B = 2, …, Z = 26.
- The pattern may involve fixed differences, alternating rules, or grouping of letters into blocks or pairs.
- We assume that the series is deliberate and has a single, consistent rule that applies across the entire sequence.

Concept / Approach:
A powerful approach with letter sequences is to look for grouping or pairing. Instead of examining only the differences between every consecutive letter, we can consider the letters in pairs and see how they relate. In this puzzle, if we group the sequence into pairs (A, F), (Z, U), (G, L), and (T, ?), a very clear pattern emerges: in each pair, the second letter is exactly five positions away from the first letter in the alphabet, and the direction alternates between forward and backward. This pair based view is simpler and more structured than trying to force a single step pattern across all seven visible letters.

Step-by-Step Solution:
Step 1: Write the sequence in pairs: (A, F), (Z, U), (G, L), and (T, ?). Step 2: Convert each letter into its alphabet position: A = 1, F = 6, Z = 26, U = 21, G = 7, L = 12, T = 20. Step 3: For the first pair (A, F), note that 6 - 1 = 5, so F is 5 letters ahead of A. Step 4: For the second pair (Z, U), note that 26 - 21 = 5, so U is 5 letters behind Z; that is a backward movement of 5 positions. Step 5: For the third pair (G, L), note that 12 - 7 = 5, so L is 5 letters ahead of G again, another forward movement by 5. Step 6: We can now see the pattern: forward +5, backward -5, forward +5, then the next pair must follow with backward -5. Step 7: Apply this rule to the last known letter T, which is the first letter of the last pair: T is the 20th letter, so 20 - 5 = 15. Step 8: The 15th letter of the alphabet is O, so the missing letter in the sequence must be O.

Verification / Alternative check:
To verify, reconstruct the sequence including the proposed answer: A, F, Z, U, G, L, T, O. Now check each pair again. A to F is +5, Z to U is -5, G to L is +5, and T to O is -5. The alternating pattern of adding 5 and subtracting 5 from the alphabet position is perfectly consistent. None of the other options (K, M, or Q) are exactly five letters behind T, so they would break this simple and clean rule. Therefore, O is the only letter that maintains the alternating plus five minus five structure.

Why Other Options Are Wrong:
K: T is the 20th letter and K is the 11th, giving a difference of 9, which does not match the consistent gap of 5 used in all previous pairs.
M: T to M corresponds to 20 - 13 = 7; again, the difference is 7 instead of 5, so this breaks the pattern.
Q: T to Q equals 20 - 17 = 3, a difference of 3, which is inconsistent with the plus or minus 5 rule established by all earlier pairs.
Thus, K, M, and Q all fail to obey the clear pair based rule.

Common Pitfalls:
Many students initially try to find a single arithmetic sequence across all eight letters, leading to confusion when no simple difference pattern seems to fit every step. Another common error is to check only the immediate neighbours, for example F to Z or U to G, and give up when the differences look irregular. The key insight is to recognise that letters can be structured in pairs rather than one long chain. Once you notice the pair wise pattern, the series becomes straightforward. This puzzle highlights the importance of trying alternative viewpoints, such as pairing, grouping by odd and even positions, or looking at mirror relationships between letters.

Final Answer:
The missing letter that correctly continues the series A, F, Z, U, G, L, T is O.