In the number series 1, 4, 13, 40, 121, 364, the next term is _______. – UGC NET Question

Each term after the first is obtained by multiplying the previous term by 3 and adding 1. We have 1 × 3 + 1 = 4, 4 × 3 + 1 = 13, 13 × 3 + 1 = 40, 40 × 3 + 1 = 121 and 121 × 3 + 1 = 364. Applying the same rule to 364 gives 364 × 3 + 1 = 1092 + 1 = 1093. This keeps the recursion exact and transparent.

Option A:
Option A gives 1087, which cannot be expressed as 364 × 3 plus a constant of 1 and would force a different operation. This is not supported by previous steps in the series. Therefore, 1087 is not consistent with the rule.

Option B:
Option B offers 1089, which is 364 × 3, omitting the addition of 1 that has occurred at every step. This makes the pattern incomplete and inconsistent. Hence, 1089 cannot be accepted.

Option C:
Option C suggests 1091, which would correspond to adding −1 after multiplying and changes the sign of the constant term. This is not observed anywhere in the series. Thus, 1091 is not appropriate.

Option D:
Option D yields 1093, exactly equal to 364 × 3 + 1, and fully respects the recursive rule defining the sequence. The extended series remains governed by a single transformation. Therefore, 1093 is the correct next term.