In the number series 3, 7, 15, 31, 63, the next term is _______. – UGC NET Question

Each term after the first is obtained by doubling the previous term and adding 1. We have 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31 and 31 × 2 + 1 = 63. Applying the same rule again gives 63 × 2 + 1 = 127. This keeps the recursive structure consistent and explains every transition in the series.

Option A:
Option A gives 127, which fits the rule "double the previous term and add one" exactly. The extended sequence 3, 7, 15, 31, 63, 127 maintains a single, simple recursive pattern. Therefore, 127 is the correct next term for this number series.

Option B:
Option B provides 125, which would correspond to subtracting 1 after doubling or using a different constant, neither of which is supported by earlier terms. This breaks the consistent "+1" part of the rule. Hence, 125 cannot be considered correct.

Option C:
Option C suggests 129, which would require adding 3 after doubling 63, changing the constant in the recursive expression. No previous step uses "+3," so this option does not follow the observed pattern. Therefore, 129 is not appropriate.

Option D:
Option D presents 130, which is 67 more than 63 and does not come from doubling and adding a fixed small constant. This makes the relationship unclear and inconsistent with the earlier rule. Thus, 130 is not the right answer.