Letter series C I S G Y – UGC NET Question

The positions follow the rule 2n² + 1 for n = 1 to 5: 2·1² + 1 = 3 (C), 2·2² + 1 = 9 (I), 2·3² + 1 = 19 (S), 2·4² + 1 = 33 ≡ 7 (G) and 2·5² + 1 = 51 ≡ 25 (Y) when reduced modulo 26. For n = 6, 2·6² + 1 = 73, which corresponds to position 21 (73 − 52 = 21), the letter U. Thus U is the only letter that fits the quadratic pattern with wrap-around.

Option A:
Option A, V, is at position 22 and does not satisfy the formula 2n² + 1 for any consecutive integer n after 5. It appears close numerically but does not arise from the defined rule. Therefore it cannot be accepted as the next term.

Option B:
Option B, W, corresponds to position 23, which again does not match the computed position for n = 6. While it is near in the alphabet, the underlying quadratic expression would have to change to justify W, which is not supported by the earlier terms.

Option C:
Option C, U, is correct because its position 21 is exactly what we obtain from 2·6² + 1 when considered modulo 26. It maintains the same mathematical rule that produced all previous letters. This continuity in the generating formula makes U the unique valid continuation.

Option D:
Option D, T, lies at position 20 and would correspond to a different input or rule. It does not satisfy the specific function used to generate earlier terms. As a result, T does not belong to this series as its next element.