UGC NET Questions (Paper – 1)

The sequence is generated by aₙ = n⁴ + n² − n for n starting from 1. Substituting n = 1, 2, 3, 4 and 5 gives 1+1−1 = 1, 16+4−2 = 18, 81+9−3 = 87, 256+16−4 = 268 and 625+25−5 = 645, which matches the given series exactly. For n = 6 we compute 6⁴+6²−6 = 1296+36−6 = 1326. Thus 1326 is the only value that preserves this quartic-plus-quadratic-minus-linear pattern.

Option A:
Option A, 1315, is close but not equal to 6⁴+6²−6. It would require subtracting 11 from the value dictated by the formula only for the sixth term. Such an adjustment is not supported by the earlier behaviour of the series and therefore makes option A incorrect.

Option B:
Option B, 1320, differs by 6 from the formula’s result and also does not satisfy n⁴+n²−n when n = 6. Choosing 1320 would arbitrarily reduce the correct term and break the functional rule connecting all terms. Hence this option cannot represent the correct continuation.

Option C:
Option C, 1323, is still not equal to 1296+36−6 and has no direct expression in terms of the established rule. It lies between some candidate values but does not come from the defined algebraic pattern. Therefore option C is not logically consistent with the observed sequence.

Option D:
Option D, 1326, matches exactly the output of the formula for n = 6. It continues the same combination of quartic, quadratic and linear components that produced all previous terms. Because this value arises naturally from the rule without modification, 1326 is the correct next term in the series.