In the number series 8, 21, 42, 71, 108, the next term is _______. – UGC NET Question

The pattern here is given by aₙ = 4n²+n+3 for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 4·1²+1+3 = 8, 4·2²+2+3 = 21, 4·3²+3+3 = 42, 4·4²+4+3 = 71 and 4·5²+5+3 = 108. For n = 6 we compute 4·6²+6+3 = 144+6+3 = 153. Thus 153 is the correct next term consistent with this quadratic rule.

Option A:
Option A, 153, matches exactly the value from aₙ = 4n²+n+3 when n = 6. It keeps the same combination of square, linear and constant parts used to generate all earlier terms. Because the relationship holds perfectly, 153 is the correct continuation.

Option B:
Option B, 143, is 10 less than the formula’s result and does not satisfy the expression for n = 6. It requires an unexplained reduction of the term, which is not supported by the pattern. Therefore 143 is not a valid choice.

Option C:
Option C, 147, is also different from 153 and cannot be obtained from the given formula without changing its constants. This would make the rule inconsistent at the final term. Hence 147 is not correct.

Option D:
Option D, 161, exceeds the computed value and similarly fails to equal 4n²+n+3 when n = 6. Using 161 would break the neat polynomial structure, so it is not the right answer.