In the number series 2, 7, 17, 37, 77, the next term is _______. – UGC NET Question

Each term is obtained by doubling the previous term and adding 3. We have 2 × 2 + 3 = 7, 7 × 2 + 3 = 17, 17 × 2 + 3 = 37 and 37 × 2 + 3 = 77. Applying the same rule to 77 gives 77 × 2 + 3 = 154 + 3 = 157. This keeps the recursive pattern uniform across all steps.

Option A:
Option A gives 155, which would require adding only 1 after doubling or using a different operation, neither of which is seen earlier. Thus, 155 is not compatible with the pattern.

Option B:
Option B offers 156, which corresponds to adding 2 after doubling 77 and again changes the constant part of the rule. This violates the consistency of "plus 3." Therefore, 156 cannot be accepted as correct.

Option C:
Option C yields 157, exactly equal to 77 × 2 + 3, and perfectly aligns with the transformation applied to each term. The sequence 2, 7, 17, 37, 77, 157 remains governed by a single simple rule. Hence, 157 is the correct next term.

Option D:
Option D suggests 159, which is 82 more than 77 and does not arise from the rule "double then add three." This introduces an arbitrary jump into the series. Therefore, 159 is not appropriate.