In the number series 1, 5, 17, 53, 161, the next term is _______. – UGC NET Question

This series is generated by the rule “multiply the previous term by 3 and add 2”. We have 1×3+2 = 5, 5×3+2 = 17, 17×3+2 = 53 and 53×3+2 = 161. Applying the same rule to 161 gives 161×3+2 = 483+2 = 485. Hence 485 is the only value that continues the sequence in strict accordance with the recursive pattern.

Option A:
Option A gives 479, which cannot be written as 161×3+2 and would require subtracting an additional amount. This contradicts the consistently “+2” adjustment after multiplication by 3 in the earlier steps. Therefore 479 is not consistent with the rule.

Option B:
Option B gives 481, corresponding to 161×3−2, which would change the sign of the constant adjustment and break the established behaviour. Thus 481 is not a valid continuation of the series.

Option C:
Option C gives 483, equal to 161×3, but this omits the “+2” that appears in every transition. This makes the rule incomplete for the last step, so 483 cannot be accepted as correct.

Option D:
Option D gives 485, exactly equal to 161×3+2. It maintains the same transformation applied in all earlier steps, keeping the pattern transparent and stable. Consequently, 485 is the correct next term in the series.