In the number series 3, 8, 23, 68, 203, the next term is _______. – UGC NET Question

The series follows the rule “multiply the previous term by 3 and subtract 1”. We have 3×3−1 = 8, 8×3−1 = 23, 23×3−1 = 68 and 68×3−1 = 203. Applying the same rule again gives 203×3−1 = 609−1 = 608. Thus 608 is the unique value that continues the series in exact agreement with the recursive transformation.

Option A:
Option A gives 608, exactly equal to 203×3−1. This preserves the pattern that every term (after the first) is obtained by tripling the previous term and then subtracting 1. Because it keeps the recurrence intact without modification, 608 is the correct next term.

Option B:
Option B gives 610, which would correspond to 203×3+1 and change the subtraction step into an addition. This contradicts the repeated “−1” adjustment seen at every earlier stage, so 610 is not consistent with the series.

Option C:
Option C gives 612, which would require 203×3+3 or another altered operation. That breaks the simple and regular rule and introduces unnecessary complexity. Therefore 612 cannot be accepted.

Option D:
Option D gives 606, implying 203×3−3. This again modifies the constant adjustment from −1 to −3, which is not supported by the previous transitions. Hence 606 is not a valid continuation.