In the number series 7, 16, 29, 46, 67, the next term is _______. – UGC NET Question

The first-level differences are 9, 13, 17 and 21. These differences form an arithmetic progression with common difference 4. To continue this structure, the next difference should be 25. Adding 25 to the last term 67 gives 92, which maintains the regular growth among the differences.

Option A:
Option A gives 88, implying a difference of 21 from 67. This simply repeats the last difference rather than increasing it, so the progression of gaps 9, 13, 17, 21, 21 breaks the +4 pattern. Therefore 88 is not consistent with the rule.

Option B:
Option B gives 92, corresponding to a difference of 25. The differences become 9, 13, 17, 21, 25, which keep increasing by 4 each time. This perfect second-level arithmetic progression shows that 92 is the correct next term.

Option C:
Option C gives 96, yielding a difference of 29 from 67. The last jump among differences then becomes 8, which is double the expected 4 and disrupts the pattern. Hence 96 cannot be accepted.

Option D:
Option D gives 98, corresponding to a difference of 31 from 67. This further distorts the difference progression and makes the final step too large. Therefore 98 is not a valid continuation.