In the number series 1, 5, 15, 19, 57, 61, the next term is _______. – UGC NET Question

This series alternates between adding 4 and multiplying by 3. Starting from 1, we have 1 + 4 = 5, 5 × 3 = 15, 15 + 4 = 19, 19 × 3 = 57 and 57 + 4 = 61. Following the same pattern, the next operation must be multiplication by 3. Thus, the next term is 61 × 3 = 183, preserving the alternating structure.

Option A:
Option A gives 181, which would require adding 120 to 61 or applying a different operation that is not indicated by any previous step. This has no relation to the alternating rule. Hence, 181 is not consistent with the pattern.

Option B:
Option B offers 182, which again cannot be produced by either adding 4 or multiplying by 3 to 61. It breaks the carefully maintained alternation of operations. Therefore, 182 is not appropriate.

Option C:
Option C yields 183, exactly equal to 61 × 3 and in full agreement with the "+4, then ×3" pattern. The sequence 1, 5, 15, 19, 57, 61, 183 remains logically coherent. Hence, 183 is the correct next term.

Option D:
Option D suggests 185, which requires adding 124 to 61 or some other arbitrary step, neither of which matches the earlier structure. This makes 185 an invalid continuation.