In the number series 4, 7, 12, 19, 28, 39, the next term is _______. – UGC NET Question

Each term can be written as n² + 3 for consecutive integers n. For n = 1, 2, 3, 4, 5 and 6, we obtain 1² + 3 = 4, 2² + 3 = 7, 3² + 3 = 12, 4² + 3 = 19, 5² + 3 = 28 and 6² + 3 = 39. The next integer is 7, so the next term should be 7² + 3 = 49 + 3 = 52. This maintains the same square-based functional rule.

Option A:
Option A gives 50, which does not correspond to the expression n² + 3 for the next integer in sequence. Using 50 would break the direct link between n and the term value. Therefore, 50 is not consistent with the pattern.

Option B:
Option B yields 52, which matches 7² + 3 and fits the established formula perfectly. The extended series 4, 7, 12, 19, 28, 39, 52 follows a single algebraic rule from n = 1 to n = 7. Hence, 52 is the correct next term.

Option C:
Option C suggests 54, which has no basis in the n² + 3 pattern for any consecutive n after 6. It introduces an unjustified deviation from the rule. Thus, 54 is not an appropriate continuation.

Option D:
Option D offers 56, which similarly fails to fit the n² + 3 relationship and appears arbitrary in the context of the given sequence. Therefore, 56 cannot be accepted as correct.