In the number series 4, 11, 22, 37, 56, the next term is _______. – UGC NET Question

The consecutive differences in the series are 7, 11, 15 and 19. These differences form an arithmetic progression with common difference 4. Therefore the next difference should be 23. Adding 23 to the last term 56 gives 79, which maintains the same second-level arithmetic structure and yields a smooth continuation.

Option A:
Option A gives 79, creating differences 7, 11, 15, 19, 23. Each difference increases by 4, so the pattern among the gaps remains consistent and clear. This makes 79 the only option that fully respects the established structure of the sequence.

Option B:
Option B gives 77, corresponding to a difference of 21 from 56. The resulting difference sequence 7, 11, 15, 19, 21 would end with a step of 2 instead of 4, breaking the uniform growth in the differences. Thus 77 does not fit the rule.

Option C:
Option C gives 81, which implies a difference of 25 from 56. That produces gaps 7, 11, 15, 19, 25, where the last increment is 6 and not 4. Consequently, 81 disrupts the simple arithmetic progression among the differences.

Option D:
Option D gives 83, yielding a difference of 27 from 56. The final increment between 19 and 27 becomes 8, which sharply departs from the steady step of 4. Therefore 83 is not a valid continuation of the series.