In the number series 6, 11, 21, 36, 56, 81, the next term is _______. – UGC NET Question

The differences between terms are 5, 10, 15, 20 and 25. These are multiples of 5 increasing by 5 each time. The next difference should therefore be 30. Adding 30 to the last term 81 gives 81 + 30 = 111, which maintains the clear pattern in the differences.

Option A:
Option A gives 107, corresponding to a difference of 26 from 81, which is not a multiple of 5 and breaks the multiples pattern. Thus, 107 is not consistent with the second-level structure.

Option B:
Option B offers 109, which would produce a difference of 28 from 81, again not a multiple of 5 and unrelated to the previous increments. Therefore, 109 cannot be accepted as correct.

Option C:
Option C yields 111, which is 30 more than 81 and completes the sequence of differences 5, 10, 15, 20, 25, 30. The pattern stays simple and mathematically sound. Hence, 111 is the correct next term.

Option D:
Option D suggests 113, giving a difference of 32 from 81, which neither follows the multiple-of-5 rule nor the linear growth seen earlier. This choice would disrupt the logic of the series. Therefore, 113 is not appropriate.