In the number series 1, 2, 5, 14, 41, 122, the next term is _______. – UGC NET Question

Each term after the first is obtained using the rule "multiply the previous term by 3 and subtract 1". We have 1 × 3 − 1 = 2, 2 × 3 − 1 = 5, 5 × 3 − 1 = 14, 14 × 3 − 1 = 41 and 41 × 3 − 1 = 122. Applying this rule again gives 122 × 3 − 1 = 366 − 1 = 365. This keeps the recursive structure consistent and elegant.

Option A:
Option A gives 362, which would require subtracting 4 after multiplication or using a different constant, something not present earlier in the series. As a result, 362 breaks the pattern.

Option B:
Option B offers 364, corresponding to subtracting 2 after multiplying 122 by 3, and again changes the constant part of the rule. Thus, 364 does not align with the "minus one" pattern.

Option C:
Option C yields 365, exactly equal to 122 × 3 − 1, and extends the rule that has been consistently applied to all previous transitions. The sequence 1, 2, 5, 14, 41, 122, 365 is logically coherent. Hence, 365 is the correct next term.

Option D:
Option D suggests 367, which would involve adding 1 rather than subtracting 1 at the end of the operation. This is not supported by the existing steps. Therefore, 367 cannot be accepted as correct.