In the number series 4, 35, 116, 271, 524, the next term is _______. – UGC NET Question

The terms of this sequence satisfy the formula (a_n = 4n^3 + n^2 - 1) for n starting from 1. For n = 1, 2, 3, 4 and 5 we have 4+1−1 = 4, 32+4−1 = 35, 108+9−1 = 116, 256+16−1 = 271 and 500+25−1 = 524. For n = 6 the same expression yields (4×6^3 + 6^2 - 1 = 864 + 36 - 1 = 899). Consequently, 899 is the correct continuation of the series.

Option A:
Option A, 899, coincides with the value produced by the formula when n = 6. It keeps both the cubic and quadratic components of the pattern intact. Because it results directly from the generating rule, 899 is the correct next term.

Option B:
Option B, 887, is 12 less than the computed value and does not equal (4×6^3 + 6^2 - 1). It would require a sudden and unjustified reduction at the final step, so 887 is not valid.

Option C:
Option C, 911, overshoots the expected value and cannot be derived from the same expression for n = 6. Selecting 911 would distort the algebraic structure of the series. Hence 911 is not the right answer.

Option D:
Option D, 923, deviates even further from the formula’s output and again fails to satisfy the rule. This would destroy the strong correspondence between index and term, so 923 is not correct.