In the number series 2, 5, 12, 23, 38, 57, the next term is _______. – UGC NET Question

The first-level differences are 3, 7, 11, 15 and 19. These differences form an arithmetic progression with common difference 4. Following this pattern, the next difference should be 23. Adding 23 to the last term 57 gives 80, so 80 is the next term that keeps both levels of the pattern consistent.

Option A:
Option A gives 76, which corresponds to a difference of 19 from 57. This simply repeats the last difference and leads to difference values 3, 7, 11, 15, 19, 19, breaking the steady increase by 4. Therefore 76 cannot be the correct continuation.

Option B:
Option B gives 80, which implies a difference of 23 from 57. The differences become 3, 7, 11, 15, 19, 23, forming a clean arithmetic progression with step 4. Hence 80 is fully consistent with the structure of the sequence and is the correct answer.

Option C:
Option C gives 82, leading to a difference of 25 from 57. That would make the final increment between differences equal to 6 instead of 4, distorting the neat second-level pattern. Thus 82 is not suitable.

Option D:
Option D gives 84, implying a difference of 27 from 57, which makes the last step among differences equal to 8. This change is too abrupt and inconsistent with the established progression, so 84 cannot be accepted.