In the number series 2, 6, 7, 21, 22, 66, 67, the next term is _______. – UGC NET Question

The series alternates between multiplying by 3 and adding 1. Starting from 2, we have 2 × 3 = 6, 6 + 1 = 7, 7 × 3 = 21, 21 + 1 = 22, 22 × 3 = 66 and 66 + 1 = 67. The next operation in this alternating pattern is multiplication by 3. Thus, the next term should be 67 × 3 = 201, which maintains the established structure.

Option A:
Option A gives 200, which cannot be obtained by either multiplying by 3 or adding 1 to 67. It introduces a new operation that is not indicated by earlier transitions. Therefore, 200 is not consistent with the observed pattern.

Option B:
Option B yields 201, exactly equal to 67 × 3, and fits the repeated alternation between "×3" and "+1". The series 2, 6, 7, 21, 22, 66, 67, 201 follows one coherent rule throughout. Hence, 201 is the correct next term.

Option C:
Option C suggests 203, which is 136 greater than 67 and does not correspond to either operation used previously. This destroys the recursive clarity of the sequence. Thus, 203 is not the right continuation.

Option D:
Option D offers 205, moving even further away and requiring an even larger and unjustified jump. This is not supported by any step in the existing pattern. Therefore, 205 cannot be regarded as correct.