In the number series 7, 36, 139, 388, 879, the next term is _______. – UGC NET Question

This series is governed by the rule aₙ = n⁴ + 2n³ + 4 with n starting at 1. For n = 1, 2, 3, 4 and 5 the expression gives 7, 36, 139, 388 and 879, matching the provided terms. Evaluating the same formula at n = 6 yields 1732. Therefore 1732 is the unique next term that preserves this quartic-plus-cubic pattern.

Option A:
Option A, 1708, is 24 less than the value obtained from aₙ = n⁴ + 2n³ + 4 when n = 6. Using 1708 would require lowering the exact polynomial result only at this index. Since no such adjustment occurs earlier, this option does not align with the pattern and is incorrect.

Option B:
Option B, 1720, is still below the required value and does not equal the formula’s output for n = 6. It partially approaches the right number but still breaks the precise functional relationship. Consequently, 1720 cannot be the correct continuation of the sequence.

Option C:
Option C, 1726, lies closer but is still 6 less than the correct value 1732. Accepting 1726 would again mean tampering with the polynomial outcome at only one term. Because the sequence is exactly modelled by aₙ = n⁴ + 2n³ + 4, any deviation at n = 6 makes this option wrong.

Option D:
Option D, 1732, is exactly the result of substituting n = 6 into the expression n⁴ + 2n³ + 4. It keeps the same structure of a dominant fourth-power term plus a cubic and constant term. As it fits perfectly into the established rule, 1732 is the correct next term.