In the number series 3, 8, 15, 24, 35, the next term is _______. – UGC NET Question

Each term in the series can be represented as n² − 1 for successive integers n starting from 2. For n = 2, 3, 4, 5 and 6 we get 2² − 1 = 3, 3² − 1 = 8, 4² − 1 = 15, 5² − 1 = 24 and 6² − 1 = 35. The next integer is 7, so the next term should be 7² − 1, which equals 49 − 1 = 48. This keeps the expression governing the series intact.

Option A:
Option A gives 46, which is not of the form n² − 1 for any integer that naturally follows 6 in the progression. Using 46 would break the simple relationship between term position and value. Hence, 46 is not consistent with the pattern.

Option B:
Option B yields 48, matching 7² − 1 and continuing the formula-based structure. The extended sequence 3, 8, 15, 24, 35, 48 clearly corresponds to 2² − 1 through 7² − 1. Therefore, 48 is the correct next term.

Option C:
Option C suggests 50, which has no direct explanation in terms of the n² − 1 rule for the next integer. It introduces a deviation from the well-defined polynomial pattern. Thus, 50 cannot be accepted as correct.

Option D:
Option D presents 52, which again does not correspond to 7² − 1 and appears arbitrary relative to the rest of the series. Choosing 52 would disrupt the simple square-based relationship. Therefore, 52 is not appropriate.