In the number series 7, 28, 99, 280, 655, the next term is _______. – UGC NET Question

The series is generated by the polynomial rule aₙ = n⁴ + 6n with n starting from 1. Substituting n = 1, 2, 3, 4 and 5 gives 7, 28, 99, 280 and 655, which exactly matches the given terms. Applying the same expression for n = 6 gives a₆ = 6⁴ + 6·6 = 1296 + 36 = 1332. Therefore 1332 is the only value that continues this polynomial pattern without changing the underlying rule.

Option A:
Option A gives 1332, which is exactly the value obtained from the formula n⁴ + 6n for n = 6. It maintains the same relationship between the index and term that produced all earlier numbers. Because no adjustment or exception is needed at the sixth term, this option correctly extends the series.

Option B:
Option B, 1308, is 24 less than the value predicted by n⁴ + 6n at n = 6. To accept 1308 we would have to reduce the correct polynomial result only at the last step, which contradicts the exact agreement seen for the first five terms. Hence this option does not respect the established pattern.

Option C:
Option C, 1320, is still below the correct value and cannot be obtained from n⁴ + 6n when n = 6. It represents a near but inaccurate approximation that breaks the strict algebraic rule behind the sequence. For a UGC NET numerical reasoning item, such a deviation means this option must be rejected.

Option D:
Option D, 1344, is 12 greater than the formula’s output and likewise cannot be produced by the same rule at n = 6. Choosing 1344 would introduce an unexplained increase in the last term, destroying the consistency of the pattern. Therefore this option is not a valid continuation of the number series.