In the number series 4, 9, 18, 23, 46, 51, the next term is _______. – UGC NET Question

This series alternates between adding 5 and multiplying by 2. Starting from 4 we have 4 + 5 = 9, 9 × 2 = 18, 18 + 5 = 23, 23 × 2 = 46 and 46 + 5 = 51. The next step should therefore apply the multiplication operation. Hence, the next term is 51 × 2 = 102, which follows the established alternation.

Option A:
Option A gives 100, which does not result from either adding 5 or multiplying by 2 to 51. It introduces a new and unsupported operation into the sequence. Therefore, 100 is not compatible with the observed pattern.

Option B:
Option B yields 102, exactly equal to 51 × 2 and in perfect agreement with the alternating "+5, then ×2" rule. The series 4, 9, 18, 23, 46, 51, 102 remains structured and predictable under this rule. Hence, 102 is the correct next term.

Option C:
Option C suggests 104, which cannot be derived from either +5 or ×2 applied to 51. It would force an arbitrary adjustment not present in any earlier step. Thus, 104 is not the correct continuation.

Option D:
Option D presents 106, which is even further from the expected result of 51 × 2. This value does not fit the consistent alternating operations used to build the series. Therefore, 106 must be rejected.