In the number series 3, 12, 27, 48, 75, the next term is _______. – UGC NET Question

The differences between consecutive terms are 9, 15, 21 and 27. These differences increase by 6 at each step, forming a simple arithmetic pattern. The next difference should therefore be 33. Adding 33 to the last term 75 gives 75 + 33 = 108, which extends the series in a consistent manner.

Option A:
Option A gives 102, which yields a difference of 27 from 75 and repeats the last difference instead of moving to 33. This breaks the steady growth by 6 in the differences. Therefore, 102 is not correct.

Option B:
Option B offers 105, whose difference from 75 is 30, not the expected 33. This slightly underestimates the predicted increment and disrupts the pattern. Hence, 105 cannot be accepted.

Option C:
Option C yields 108, which is 33 more than 75 and continues the difference sequence 9, 15, 21, 27, 33 as an arithmetic progression. This keeps the series logically structured. Thus, 108 is the correct next term.

Option D:
Option D suggests 111, giving a difference of 36 from 75, overshooting the required increment and making the sequence irregular. Therefore, 111 is not appropriate.