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

The differences are 6, 9, 12 and 15, which form an arithmetic pattern increasing by 3 each time. The next difference should therefore be 18. Adding 18 to the last term 48 gives 66. Hence, 66 is the correct next term in the series.

Option A:
Option A is 60, which gives a difference of 12 from 48, repeating an earlier step instead of moving to 18. This disrupts the neat progression of 6, 9, 12, 15, 18. Therefore, 60 is not correct.

Option B:
Option B equals 66 and produces the expected new difference of 18. With this choice, the difference sequence becomes 6, 9, 12, 15, 18, which maintains a clear rule of adding 3 each time. Thus, 66 is the valid continuation.

Option C:
Option C is 72, implying a difference of 24, which jumps beyond the required 18 and overshoots the pattern. No prior step supports such a large increase. Hence, 72 cannot be chosen.

Option D:
Option D is 78, giving a difference of 30 from 48, which is even further away from the expected 18. This would completely break the second-level arithmetic structure. Therefore, 78 is not appropriate.