In the number series 5, 9, 15, 23, 33, the next term is _______. – UGC NET Question

The differences between successive terms are 4, 6, 8 and 10. These differences form an arithmetic pattern increasing by 2 each time. The next difference should therefore be 12. Adding 12 to the last term 33 gives 33 + 12 = 45, which extends the series consistently.

Option A:
Option A gives 43, corresponding to a difference of 10 from 33, which simply repeats the last difference rather than increasing it. This breaks the second-level arithmetic progression. Hence, 43 does not follow the intended pattern.

Option B:
Option B yields 45, which is 12 more than 33 and maintains the difference sequence 4, 6, 8, 10, 12. This preserves the clear, systematic growth at the level of differences. Therefore, 45 is the correct next term in the series.

Option C:
Option C suggests 47, which would produce a difference of 14 and jump beyond the expected increment. This destroys the steady increase by 2 units in the differences. Thus, 47 is not a valid continuation.

Option D:
Option D offers 49, giving a difference of 16 from 33 and deviating even further from the planned pattern. Including 49 would make the sequence erratic. Therefore, 49 cannot be regarded as correct.