Letter series A D I P – UGC NET Question

The positions of these letters are A(1), D(4), I(9) and P(16). These correspond to 1², 2², 3² and 4². The next square number is 5² = 25, which corresponds to Y. Thus Y is the only letter that continues the pattern based on perfect squares.

Option A:
Option A, W, is at position 23, which is not a perfect square. It cannot be represented as n² for a positive integer n. Therefore W does not follow the underlying square-number rule.

Option B:
Option B, X, corresponds to position 24, which again is not a perfect square. Selecting X would abandon the clear pattern of using square positions. Hence X cannot logically follow P in this sequence.

Option C:
Option C, Z, is at position 26, also not a perfect square. While it is near 25, the pattern is exact and not approximate. Because 26 does not equal any n², Z fails to satisfy the generating rule.

Option D:
Option D is correct because Y occupies position 25, exactly 5². It extends the series of square-number positions from 1² through 4² to 5². This perfect alignment with the numerical pattern makes Y the valid next term.