In the letter pair series AT, DR, GP, JN, ?, which of the following pairs should come next to complete the pattern?

Introduction / Context:
The pair series AT, DR, GP, JN, ?, involves two letter pairs where the first and second letters move in opposite directions through the alphabet with constant steps. Identifying these two simple numeric progressions allows us to determine the next pair easily.

Given Data / Assumptions:

• Pairs: AT, DR, GP, JN, ?
• Alphabet positions A 1 to Z 26.
• We treat first letters and second letters separately.

Concept / Approach:
We take the first letters A, D, G, J, ? as one sequence, and the second letters T, R, P, N, ? as another. Converting letters into numeric positions reveals that the first letters move forward by a constant positive step while the second letters move backward by a constant negative step. Extending both sequences by one step gives the required pair.

Step-by-Step Solution:
Step 1: First letters are A, D, G, J. Step 2: Positions: A 1, D 4, G 7, J 10. Step 3: Differences: 4 minus 1 equals 3, 7 minus 4 equals 3, and 10 minus 7 equals 3. So the first letters increase by 3. Step 4: Next first letter is 10 plus 3 equals 13, which is M. Step 5: Second letters are T, R, P, N. Step 6: Positions: T 20, R 18, P 16, N 14. Step 7: Differences: 18 minus 20 equals minus 2, 16 minus 18 equals minus 2, and 14 minus 16 equals minus 2. So the second letters decrease by 2. Step 8: Next second letter is 14 minus 2 equals 12, which is L. Step 9: Therefore the missing pair is ML.

Verification / Alternative check:
Write all pairs in numeric form: AT 1,20; DR 4,18; GP 7,16; JN 10,14; ML 13,12. In the first column, we have 1, 4, 7, 10, 13, which follows a plus 3 pattern. In the second column, we have 20, 18, 16, 14, 12, which follows a minus 2 pattern. No other option in the list matches both of these progressions simultaneously.

Why Other Options Are Wrong:
MJ has J 10 as the first letter instead of M 13 and J 10 instead of L 12, so it does not respect either pattern. MN has the correct first letter M 13 but second letter N 14, which breaks the minus 2 progression. MK has L replaced by K 11, which would correspond to a step of minus 3 instead of minus 2. NL shifts the first letter to N 14 and no longer fits the plus 3 sequence.

Common Pitfalls:
Learners sometimes assume that both letters move with the same step size or in the same direction. Others may only check the first letters and choose a pair starting with M without confirming the behaviour of the second letters. Separating the two sequences and working numerically avoids these pitfalls.

Final Answer:
The pair that correctly completes the series is ML.