In the number series 2, 98, 736, 3086, 9398, the next term is _______. – UGC NET Question

This series is generated by the rule aₙ = 3n⁵ + n² − 2 with n starting at 1. Substituting n = 1, 2, 3, 4 and 5 yields 2, 98, 736, 3086 and 9398, which correspond exactly to the given terms. For n = 6 the same expression produces 23362. Therefore 23362 is the unique value that continues this high-degree polynomial pattern.

Option A:
Option A, 23278, is 84 less than the value obtained from aₙ = 3n⁵ + n² − 2 at n = 6. Choosing 23278 would require a large downward adjustment of the correct result only at this stage. Since earlier terms match the formula exactly, this option does not conform to the established rule and is incorrect.

Option B:
Option B, 23362, matches exactly the number produced by the expression when n = 6. It preserves the dominance of the fifth-power term together with the smaller quadratic and constant components. Because it fits perfectly into the same pattern that explains all previous terms, 23362 is the correct answer.

Option C:
Option C, 23398, is 36 greater than the required value and cannot be written as 3n⁵ + n² − 2 for n = 6. Adopting 23398 would arbitrarily increase the term at the final position, breaking the algebraic consistency. Thus option C is not a valid continuation of the sequence.

Option D:
Option D, 23434, deviates even more from the computed value and likewise fails to satisfy the rule at n = 6. Using 23434 would destroy the precise functional link between index and term. Hence option D is incorrect.