UGCNET Questions

The pattern in this series is based on increasing differences that themselves double each time. The differences between successive terms are 3, 6, 12 and 24. Each new difference is twice the previous one, giving the next difference as 48. When this difference of 48 is added to the last term 46, the next term becomes 94. Thus, 94 continues the established pattern of doubling increments.

Option A:
Option A, 88, would correspond to adding 42 to 46, which does not match the doubling pattern of 3, 6, 12 and 24. It ignores the rule that each difference is twice the previous difference.

Option B:
Option B, 90, arises if we add 44 to 46, but there is no consistent reason in the earlier terms to justify a difference of 44. It breaks the strict doubling of the gaps.

Option C:
Option C, 94, uses a difference of 48, which is double the previous difference of 24. This respects the second order structure of the series and produces a term fully consistent with the pattern.

Option D:
Option D, 98, assumes an increase of 52, again not related to the repeated doubling of the differences. It introduces a new rule that is not supported by the earlier terms.

The pattern in the series is that each term is obtained by doubling the previous term and adding 1. Specifically, 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31 and 31 × 2 + 1 = 63. Continuing this rule, the next term is 63 × 2 + 1 = 127. Hence, 127 is the only number that preserves the established doubling plus one pattern.

Option A:
Option A, 95, could come from adding 32 to 63, but there is no basis for adding a fixed difference when the earlier transitions are multiplicative with an extra 1. It breaks the observed rule of doubling.

Option B:
Option B applies the same operation used at every step of the series, doubling 63 and then adding 1. This keeps the structure consistent across all terms and therefore correctly predicts the next number.

Option C:
Option C, 125, is close numerically but would require adding 62, again inconsistent with the doubling plus one pattern seen earlier.

Option D:
Option D, 119, might reflect adding 56, but such a jump is not supported by any of the prior steps in the sequence.