In the number series 3, 6, 12, 21, 33, 48, the next term is _______. – UGC NET Question

The differences between consecutive terms are 3, 6, 9, 12 and 15. These differences increase by 3 each time, forming a simple arithmetic pattern at the second level. The next difference should therefore be 18. Adding 18 to the last term 48 gives 48 + 18 = 66, which continues the series in a consistent way.

Option A:
Option A gives 60, corresponding to a difference of 12 from 48, which repeats an earlier increment and fails to progress to 18. This disrupts the growth of the differences. Hence, 60 is not correct.

Option B:
Option B offers 63, whose difference from 48 is 15, again repeating the last difference instead of increasing it. This is not compatible with the pattern. Therefore, 63 cannot be accepted.

Option C:
Option C suggests 64, giving a difference of 16 from 48, which does not fit the multiples-of-three structure in the differences. This makes the pattern irregular. Thus, 64 is not appropriate.

Option D:
Option D yields 66, which is 18 more than 48 and extends the differences to 3, 6, 9, 12, 15, 18. This preserves the second-level arithmetic progression, so 66 is the correct next term.