In the single-letter alphabet series F, I, M, P, T, which letter should appear next to continue the sequence?

Introduction / Context:
This problem involves a series of single letters from the English alphabet: F, I, M, P, T. The task is to find the logical next letter. Such questions are simpler to read than multi-letter series but still require careful analysis of the jumps between letters. They are a quick test of numerical reasoning using alphabet positions rather than numerical digits directly.

Given Data / Assumptions:

• Series: F, I, M, P, T, ?.• Each term is a single capital letter.• There is likely a repeating pattern in the differences between positions.• The alphabet is mapped with A=1, B=2, ..., Z=26.

Concept / Approach:
We convert each letter into a number, find the difference between consecutive terms, and then look for a pattern in these differences. If the differences themselves form a simple sequence, such as alternating values, we can apply this structure to predict the next term. Recognising whether the increments repeat or grow steadily is a crucial part of solving such series.

Step-by-Step Solution:
Positions: F=6, I=9, M=13, P=16, T=20.Differences: 9 − 6 = 3, 13 − 9 = 4, 16 − 13 = 3, 20 − 16 = 4.So the pattern of increments is +3, +4, +3, +4, alternating.The next increment should therefore be +3 again.Next letter position = 20 + 3 = 23, which is W.

Verification / Alternative check:
We can re-express the sequence as 6, 9, 13, 16, 20, 23. The second differences (the differences between the differences) alternate between +1 and −1, but the more important observation is the repeating pattern +3, +4. When we continue this pattern, 20 + 3 = 23 emerges naturally. No other letter choice from the options fits this rule as neatly as W.

Why Other Options Are Wrong:
Choosing X, Y or Z would imply increments of +4, +5 or +6 from T, none of which match the established alternating pattern of +3 and +4. These choices would break the neat alternation in the differences of letter positions. Therefore, they can be rejected once the incremental rule has been correctly identified.

Common Pitfalls:
Sometimes candidates assume a constant increment without checking carefully, which would make them choose X (+3 and +4 averaged as +3.5). Others may look at rough visual distances between letters without calculating exact numeric positions. To avoid such mistakes, always compute precise differences and look for simple repeating structures.

Final Answer:
W