In the number series 4, 9, 17, 35, 69, the next term is _______. – UGC NET Question

The rule for this series alternates between multiplying by 2 and adding 1, and multiplying by 2 and subtracting 1. Specifically, 4×2+1 = 9, 9×2−1 = 17, 17×2+1 = 35 and 35×2−1 = 69. Following this alternation, the next step must again be “×2+1”. Thus, the next term is 69×2+1 = 139.

Option A:
Option A gives 137, which would correspond to 69×2−1. That operation was used in the previous step and would break the established alternation between “+1” and “−1” adjustments. Therefore 137 does not preserve the correct recursive pattern.

Option B:
Option B gives 141, which cannot be obtained from 69 by a simple “×2±1” rule. It would require 69×2+3, introducing a new constant and disrupting the elegant ±1 structure. Hence 141 is not a valid continuation.

Option C:
Option C gives 139, exactly equal to 69×2+1. This follows the alternating rule “+1, −1, +1, −1, +1” consistently from term to term. Because it respects the specific recursive behaviour, 139 is the correct next term in the series.

Option D:
Option D gives 143, which would equal 69×2+5 and bring in a new additive adjustment that has not appeared earlier. This contradicts the simple and regular nature of the rule, so 143 cannot be accepted.