In the number series 1, 4, 13, 40, 121, the next term is _______. – UGC NET Question

Each term after the first is three times the previous term plus 1. We see 1×3+1 = 4, 4×3+1 = 13 and 13×3+1 = 40, and 40×3+1 = 121. Applying the same rule gives 121×3+1 = 363+1 = 364. Therefore, 364 is the correct next term.

Option A:
Option A preserves the recursive formula exactly, producing 364 from 121×3+1. The series 1, 4, 13, 40, 121, 364 remains internally consistent with a single clear rule. Hence, this option is correct.

Option B:
Option B is 360, which would require subtracting 3 after tripling, not adding 1. This contradicts the pattern seen in earlier steps. Therefore, 360 is not suitable.

Option C:
Option C is 400, which has no direct link with the 3×n+1 structure. It appears as a round number but does not arise from the required operation. Thus, 400 cannot be accepted.

Option D:
Option D is 500, an even larger value that also fails to result from 121×3+1. Choosing 500 would completely ignore the established multiplication-plus-one pattern. Therefore, this option is incorrect.