In the number series 7, 18, 33, 52, 75, the next term is _______. – UGC NET Question

The differences between successive terms are 11, 15, 19 and 23. These differences form an arithmetic progression with a common difference of 4. Therefore the next difference should be 27. Adding 27 to 75 gives 102 as the next term in the series. This choice keeps both the series and the pattern of gaps internally consistent.

Option A:
Option A would create a difference of 23 from 75, so the differences would be 11, 15, 19, 23, 23. The last two gaps are equal, which breaks the rule that each difference increases by 4. Hence 98 cannot be justified by the underlying pattern.

Option B:
Option B uses a difference of 27, giving the sequence of gaps 11, 15, 19, 23, 27. Each step increases by 4, which matches the observed second-level arithmetic progression. As this option uniquely preserves the pattern, 102 is correctly identified as the next term.

Option C:
Option C would produce a difference of 29 from 75, giving gaps 11, 15, 19, 23, 29. The jump from 23 to 29 is 6 rather than 4, which distorts the arithmetic pattern among the differences. Therefore 104 is not a valid continuation.

Option D:
Option D corresponds to a difference of 21 from 75, so the last increment decreases instead of increasing to 27. This contradicts the steadily rising nature of the gaps. Thus 96 does not follow the logic of the series.