What is the next letter in the following alternating alphabetic sequence: N, O, M, P, L, Q, K, R, ?

Introduction / Context:
Alphabet series questions test the ability to recognise patterns in the positions of letters. Often, the sequence involves adding and subtracting certain numbers in a repeating pattern. In this example, the letters N, O, M, P, L, Q, K, R are given and we must find the next letter. The pattern is not a simple forward movement; instead, it alternates between increasing and decreasing positions in a regular way.

Given Data / Assumptions:
- Given sequence: N, O, M, P, L, Q, K, R, ?
- The letters correspond to positions in the alphabet: A=1, B=2, C=3, ..., Z=26.
- We assume a consistent numeric pattern governs the movement from one letter to the next.
- Our goal is to identify that pattern and use it to find the missing letter.

Concept / Approach:
The strategy is to convert each letter to its numerical position and then examine the differences between successive terms. If these differences follow a regular rule, we extrapolate that rule to predict the next term. In many reasoning questions, the series alternates between adding and subtracting numbers that follow a simple pattern, such as increasing odd numbers. Recognising that pattern leads directly to the answer.

Step-by-Step Solution:
Step 1: Write the alphabetical positions: N=14, O=15, M=13, P=16, L=12, Q=17, K=11, R=18. Step 2: Compute each difference: 14 to 15 is +1, 15 to 13 is −2, 13 to 16 is +3, 16 to 12 is −4, 12 to 17 is +5, 17 to 11 is −6, 11 to 18 is +7. Step 3: Note the pattern: the sign alternates (+, −, +, −, +, −, +) and the absolute values form an increasing sequence 1, 2, 3, 4, 5, 6, 7. Step 4: The next difference should therefore be −8 (continuing the +, − pattern and increasing the magnitude by 1). Step 5: Apply −8 to the last letter. R is position 18. Subtracting 8 gives 18 − 8 = 10. The 10th letter of the alphabet is J. So the missing letter is J.

Verification / Alternative check:
Recheck the series with the newly found term included: N(14), O(15), M(13), P(16), L(12), Q(17), K(11), R(18), J(10). Differences are +1, −2, +3, −4, +5, −6, +7, −8. The pattern of alternating signs and increasing absolute values holds perfectly. This confirms that the choice of J fits the consistent rule and is not random.

Why Other Options Are Wrong:
- "S" (19) would give a difference of +1 from R (18), breaking the established pattern.
- "I" (9) would produce a difference of −9 from R, which does not follow the −8 required by the pattern.
- "T" (20) would give +2 from R, again inconsistent with the expected −8 step.
Therefore, none of these matches the regular alternation observed in the original sequence.

Common Pitfalls:
Learners may initially look only at the forward movements and miss the alternating plus and minus pattern. Some may try to guess the answer based on approximate positions instead of checking the numeric differences carefully. Writing down the actual alphabet positions and explicitly listing the differences is the safest approach. Once the alternating pattern is recognised, similar problems become much easier to solve accurately and quickly.

Final Answer:
The next letter in the sequence N, O, M, P, L, Q, K, R is J.