In the number series 8, 43, 130, 293, 556, the next term is _______. – UGC NET Question

The series follows the rule (a_n = 4n^3 + 2n^2 + n + 1) for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 8, 43, 130, 293 and 556, which match the terms given. For n = 6 we compute (4×6^3 + 2×6^2 + 6 + 1 = 864 + 72 + 6 + 1 = 943). Hence 943 is the correct next term.

Option A:
Option A, 931, is 12 less than the value provided by the formula and does not equal (4×6^3 + 2×6^2 + 6 + 1). It indicates an unsupported decrease at the final term, so 931 is not valid.

Option B:
Option B, 943, matches exactly the output of the expression for n = 6. It maintains the balance between the cubic, quadratic and linear components, keeping the sequence structurally sound. Therefore 943 is the correct continuation.

Option C:
Option C, 955, overshoots the computed value and cannot be obtained from the given rule. Selecting 955 would artificially inflate the term and disrupt the algebraic pattern. Hence 955 is not correct.

Option D:
Option D, 961, deviates even further from 943 and again fails to satisfy the formula. Using 961 would destroy the precise relationship between n and a_n, so it is not an appropriate choice.