A letter series is given with one term missing. Select the letter that will complete the series: A, D, I, P, ?

Introduction / Context:
This question belongs to the category of alphabet series. Instead of numbers, letters are arranged in a particular logical order. You must identify the hidden pattern and then use it to find the missing letter. Here, the pattern is based on the positions of letters in the English alphabet and the sequence of perfect squares.

Given Data / Assumptions:
- The given series is: A, D, I, P, ?
- We know the positions of these letters in the alphabet: A = 1, D = 4, I = 9, P = 16.
- We need to find the fifth letter that logically continues this pattern.

Concept / Approach:
For alphabet series questions, a very useful strategy is to convert letters into their numeric positions: A = 1, B = 2, C = 3 and so on. Once we look at the numeric pattern, it is often easier to notice familiar number sequences like odd numbers, even numbers, prime numbers or perfect squares. After identifying the numeric pattern, we convert back to the corresponding letter for the final answer.

Step-by-Step Solution:
Step 1: Write the positions of the given letters. A → 1, D → 4, I → 9, P → 16. Step 2: Observe the numeric sequence: 1, 4, 9, 16. Step 3: Recognise that these are perfect squares: 1^2, 2^2, 3^2, 4^2. Step 4: The next number should naturally be the next perfect square, that is 5^2 = 25. Step 5: Find the 25th letter of the alphabet: A=1, B=2, ..., Y=25, Z=26. So the 25th letter is Y. Step 6: Replace the question mark with Y to complete the series.

Verification / Alternative check:
Check the consistency: 1^2 = 1 (A), 2^2 = 4 (D), 3^2 = 9 (I), 4^2 = 16 (P), 5^2 = 25 (Y). Each step follows the same pattern of perfect squares. No other option matches this clean and simple rule. This confirms that Y is the only valid continuation.

Why Other Options Are Wrong:
- U: Position 21, which is not a perfect square in this context.
- R: Position 18, not a perfect square and does not follow the 1, 4, 9, 16 sequence.
- W: Position 23, also unrelated to perfect squares.
Since the underlying rule is based on perfect squares of natural numbers, any letter whose position is not a perfect square cannot be correct.

Common Pitfalls:
Many learners try to look only at the difference between positions (for example, +3, +5, +7) and may fail to generalise the rule. Others may guess based on visual familiarity with certain letter pairs. Always convert letters to numbers and search for known numerical patterns such as squares, cubes, primes or arithmetic progressions. This systematic approach quickly reveals the structure.

Final Answer:
The missing term in the series is the letter Y.