In the number series 1, 28, 153, 496, 1225, the next term is _______. – UGC NET Question

This series is described by the rule (a_n = 2n^4 - n^2) for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 2−1 = 1, 32−4 = 28, 162−9 = 153, 512−16 = 496 and 1250−25 = 1225, which matches the given list. For n = 6 we compute (2×6^4 - 6^2 = 2×1296 - 36 = 2592 - 36 = 2556). Therefore 2556 is the correct continuation of the quartic pattern.

Option A:
Option A, 2528, is 28 less than the formula’s output and does not equal (2×6^4 - 6^2). It would force an arbitrary downward adjustment at the last term, which is inconsistent with the rule. Hence 2528 is not a valid next term.

Option B:
Option B, 2556, matches exactly the value produced by (a_n = 2n^4 - n^2) when n = 6. It maintains the same combination of quartic and quadratic parts seen in all earlier terms. For this reason, 2556 is the correct answer.

Option C:
Option C, 2592, corresponds to (2×6^4) alone and ignores the subtraction of (6^2). That omission breaks the established formula. Thus 2592 does not correctly extend the sequence.

Option D:
Option D, 2616, is even larger and cannot be written as (2n^4 - n^2) for the next integer n. Adopting 2616 would make the pattern inconsistent, so it is not correct.