In the number series 7, 26, 63, 124, the next term is _______. – UGC NET Question

Each term in the series can be written as n³ − 1 for successive integers n. For n = 2, 3, 4 and 5 we get 2³ − 1 = 7, 3³ − 1 = 26, 4³ − 1 = 63 and 5³ − 1 = 124. The next integer is 6, so the next term should be 6³ − 1. This equals 216 − 1 = 215, which maintains the same cubic minus one relationship.

Option A:
Option A gives 215, which is precisely 6³ − 1 and continues the formula applied in generating all previous terms. The series 7, 26, 63, 124, 215 clearly follows the rule n³ − 1 for n = 2 to 6. Hence, 215 is the logically correct next term.

Option B:
Option B offers 216, which is 6³ but does not follow the "minus one" adjustment that characterises every earlier term. Choosing 216 would change the defining rule of the sequence. Therefore, 216 is not consistent with the pattern.

Option C:
Option C presents 220, which has no direct connection with the values of n³ − 1 for consecutive integers. It appears as a random large number without algebraic justification in this context. Thus, 220 is not a valid continuation.

Option D:
Option D gives 230, which similarly does not correspond to any n³ − 1 in the progression and does not respect the underlying structure. Including 230 would make the series irregular and conceptually weak. Hence, it cannot be considered correct.