In the number series 3, 5, 9, 17, 33, the next term is _______. – UGC NET Question

Each term after the first is obtained by doubling the previous term and subtracting 1. We have 3×2−1 = 5, 5×2−1 = 9, 9×2−1 = 17 and 17×2−1 = 33, confirming the rule. Applying it again gives 33×2−1 = 66−1 = 65. Hence, 65 is the correct next term.

Option A:
Option A is 63, which would require subtracting 3 from 33×2, not 1. The series consistently subtracts 1, so altering that constant is unjustified. Therefore, 63 is incorrect.

Option B:
Option B is 64, implying that we simply double 33 and subtract 2. Such a modification has no support from the earlier steps. Thus, 64 cannot match the pattern.

Option C:
Option C equals 65 and follows the rule 33×2−1 exactly. The extended sequence 3, 5, 9, 17, 33, 65 is perfectly consistent with the defined operation. This makes 65 the valid continuation.

Option D:
Option D is 67, which would result from 33×2+1 and introduces addition instead of subtraction. Since all previous transitions subtracted 1, this change breaks the rule. Therefore, 67 is not appropriate.