In the number series 3, 4, 6, 10, 18, 34, the next term is _______. – UGC NET Question

Each term after the first is obtained by doubling the previous term and subtracting 2. We see 3 × 2 − 2 = 4, 4 × 2 − 2 = 6, 6 × 2 − 2 = 10, 10 × 2 − 2 = 18 and 18 × 2 − 2 = 34. Applying the same rule to 34 yields 34 × 2 − 2 = 68 − 2 = 66. This keeps the recursive structure intact.

Option A:
Option A gives 62, which would correspond to subtracting 6 after doubling 34 and introduces a new constant that does not appear in earlier steps. Thus, 62 is not consistent with the recursive rule.

Option B:
Option B offers 64, equal to 34 × 2 − 4, which again changes the subtractive constant and conflicts with the uniform "minus 2" operation. Therefore, 64 cannot be accepted as correct.

Option C:
Option C yields 66, exactly equal to 34 × 2 − 2, and fits the observed pattern at every stage. The series 3, 4, 6, 10, 18, 34, 66 remains governed by a single clear transformation. Hence, 66 is the correct next term.

Option D:
Option D suggests 68, which is simply 34 × 2 and omits the subtraction of 2 found throughout the series. This breaks the rule that defines the sequence. Therefore, 68 is not appropriate.