In the number series 1, 11, 35, 79, 149, the next term is _______. – UGC NET Question

The terms follow the rule aₙ = n³+n²−1 for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 1+1−1 = 1, 8+4−1 = 11, 27+9−1 = 35, 64+16−1 = 79 and 125+25−1 = 149. For n = 6 the formula yields 216+36−1 = 251. Thus 251 is the only number that continues this cubic-plus-square-minus-one pattern consistently.

Option A:
Option A, 241, is 10 less than the value obtained from the formula for n = 6. It does not satisfy aₙ = n³+n²−1 and so fails to extend the pattern logically. Therefore 241 cannot be the correct answer.

Option B:
Option B, 251, matches exactly the result of applying the rule with n = 6. It maintains the same combination of n³ and n² seen in all the earlier terms. Because the algebraic structure remains unchanged, 251 is the correct continuation of the series.

Option C:
Option C, 245, is also different from the calculated value and would require altering the constant term in the expression. That change has no support in the given data, so 245 is not a valid next term.

Option D:
Option D, 259, is larger than the correct value and again does not come from n³+n²−1 when n = 6. Using 259 would break the very precise pattern built into the sequence, making it an incorrect option.