In the number series 9, 21, 39, 63, 93, the next term is _______. – UGC NET Question

The consecutive differences are 12, 18, 24 and 30. These differences form an arithmetic progression with common difference 6. Therefore the next difference should be 36. Adding 36 to the last term 93 gives 129, so 129 continues the series in line with the observed second-level pattern.

Option A:
Option A gives 123, which implies a difference of 30 from 93. That would repeat the last difference and make the sequence of gaps 12, 18, 24, 30, 30, breaking the steady increment by 6. Thus 123 is not appropriate.

Option B:
Option B gives 126, corresponding to a difference of 33 from 93. In that case the last increase among differences would be only 3, not 6, distorting the structure. Therefore 126 does not fit the rule.

Option C:
Option C gives 129, implying a difference of 36 from 93. The difference sequence becomes 12, 18, 24, 30, 36, a clean arithmetic progression with constant step 6. This strong internal consistency makes 129 the correct next term.

Option D:
Option D gives 132, leading to a difference of 39 from 93. That makes the last increment among differences equal to 9, which is incompatible with the constant step of 6. Hence 132 cannot be accepted.