In the number series 3, 4, 6, 9, 13, 18, the next term is _______. – UGC NET Question

The differences between consecutive terms are 1, 2, 3, 4 and 5. These differences increase by 1 at each step, forming a simple arithmetic sequence. To continue this pattern, the next difference should be 6. Adding 6 to the last term 18 yields 18 + 6 = 24. This ensures that the growth at the level of differences remains smooth and systematic.

Option A:
Option A gives 22, which corresponds to a difference of 4 from 18 and repeats an earlier increment instead of moving to 6. This disrupts the steadily increasing sequence of differences. Therefore, 22 is not consistent with the pattern.

Option B:
Option B offers 23, giving a difference of 5, which again has already appeared in the series and fails to advance the difference pattern to 6. Thus, 23 cannot be accepted as correct.

Option C:
Option C yields 24, which is 6 more than 18 and extends the differences to 1, 2, 3, 4, 5, 6 in order. This maintains a clear and logical structure at the second level. Hence, 24 is the correct next term.

Option D:
Option D suggests 25, creating a difference of 7 from 18 and jumping beyond the expected increment. This makes the difference progression irregular. Therefore, 25 is not a valid continuation.