A F Z U G L T _ Find the next letter in the above given letter series?

Concept: When a letter series is grouped into consecutive pairs of two letters, the second letter of each pair is obtained by shifting the first letter's alphabet position by a fixed number of places. Across successive pairs, the direction of this shift alternates between forward (+) and backward (−) while the shift size itself stays the same.

Application:

1. Convert each letter to its position in the alphabet (A = 1, B = 2, ... Z = 26): A = 1, F = 6, Z = 26, U = 21, G = 7, L = 12, T = 20.

2. Group the eight letters into four consecutive pairs: (A, F), (Z, U), (G, L), (T, _).

3. Find the shift within each of the three complete pairs: A to F is +5, Z to U is −5, G to L is +5.

4. The shift direction alternates pair by pair (+5, −5, +5, ...), so the fourth pair must use −5.

5. Apply −5 to T (position 20): 20 − 5 = 15, which is the letter O.

Cross-check:

1. Rebuilding the series from A using this rule reproduces every given letter exactly: A(1) +5→ F(6); Z(26) −5→ U(21); G(7) +5→ L(12); T(20) −5→ O(15) — confirming O completes the series.

Answer: O