In the number series 4, 11, 24, 45, 76, the next term is _______. – UGC NET Question

The first-level differences are 7, 13, 21 and 31. The second-level differences are 6, 8 and 10, which increase by 2 each time. Continuing this pattern, the next second-level difference should be 12, so the next first-level difference becomes 31 + 12 = 43. Adding 43 to the last term 76 gives 119, making 119 the only value that preserves the consistent second-level arithmetic structure.

Option A:
Option A gives 119, which fits the calculated first-level difference of 43 and keeps the second-level differences as 6, 8, 10, 12. This maintains a neat progression where the growth of the gaps is itself arithmetic. Because both layers of the pattern remain intact, 119 is the correct continuation of the series.

Option B:
Option B gives 115, which would imply a difference of 39 from 76. That would make the second-level differences 6, 8, 10 and 8, breaking the steady increase by 2 and introducing an inconsistency. Hence 115 does not follow the underlying logic of the sequence.

Option C:
Option C gives 123, corresponding to a difference of 47 from 76. This would yield second-level differences 6, 8, 10 and 16, which jumps too sharply and does not respect the +2 progression. Therefore 123 cannot be accepted as the next term.

Option D:
Option D gives 127, leading to a difference of 51 from 76. The resulting second-level differences become 6, 8, 10 and 20, distorting the smooth pattern of increase. Thus 127 is not compatible with the observed structure of the series.