In the number series 8, 53, 208, 593, 1376, the next term is _______. – UGC NET Question

This sequence follows the rule aₙ = 2n⁴ + 5n² + 1 with n beginning at 1. For n = 1, 2, 3, 4 and 5 the expression gives 8, 53, 208, 593 and 1376, which are exactly the provided terms. Applying the same formula to n = 6 results in 2773. Therefore 2773 is the unique next term that maintains this quartic pattern with a quadratic adjustment.

Option A:
Option A, 2749, is 24 less than the value produced by aₙ = 2n⁴ + 5n² + 1 at n = 6. To obtain 2749 we would have to reduce the correct polynomial result arbitrarily for the sixth term. This is not supported by any change in the earlier sequence, so option A is incorrect.

Option B:
Option B, 2757, is still lower than the required value and does not match the formula’s output for n = 6. While numerically close, it fails to respect the exact algebraic structure of the sequence. Hence option B does not correctly continue the series.

Option C:
Option C, 2765, lies closer but remains 8 below the correct value 2773. Accepting 2765 would again mean departing from the precise polynomial expression only at the final term. Because the rule explains each previous entry perfectly, option C cannot be considered correct.

Option D:
Option D, 2773, equals exactly the value obtained when n = 6 is substituted into 2n⁴ + 5n² + 1. It preserves both the dominant quartic term and the quadratic contribution along with the constant term. As it fits seamlessly into the same pattern, 2773 is the correct next term in the series.