UGCNET Questions

The pattern in the series is that each term increases by 3. From 4 to 7 the difference is 3, from 7 to 10 it is 3 and from 10 to 13 it is again 3. To continue this arithmetic progression, we add 3 to the last term 13. That gives 13 + 3 = 16 as the next term.

Option A:
Option A keeps the constant difference of 3 between consecutive terms, which is the defining rule of this series. It extends the pattern 4, 7, 10, 13 in a straightforward way. Because it is obtained by applying the same operation as before, 16 is the only value that fits the given progression.

Option B:
Option B, 17, would require an increase of 4 from 13, which breaks the uniform +3 difference observed in the earlier steps. It introduces a new rule that is not supported by the given data.

Option C:
Option C, 18, implies adding 5 to 13 and similarly fails to maintain the steady increment of 3. It cannot be justified from the structure of the sequence.

Option D:
Option D, 19, would mean adding 6 to 13, making the jump much larger than any of the previous differences and clearly inconsistent with the pattern.

The given series increases by a constant difference of 3 between successive terms: 2 to 5, 5 to 8 and 8 to 11. To continue the same pattern, we add 3 to the last term 11. This gives 11 + 3 = 14 as the next number in the sequence. Since the rule is consistent for all previous terms, 14 uniquely fits the observed arithmetic progression.

Option A:
Option A, 13, would require a difference of 2 from 11, which breaks the established +3 pattern observed throughout the series. Choosing 13 ignores the constant increment that defines the given progression. Therefore, it is not consistent with the rule governing the sequence.

Option B:
Option B, 14, maintains the constant difference of +3 between consecutive terms, which is the key feature of this arithmetic progression. It is obtained directly by adding 3 to 11, and thus matches the pattern seen in all earlier steps. This makes 14 the logically correct continuation of the series.

Option C:
Option C, 15, would imply adding 4 to 11, which is inconsistent with the earlier differences of 3. Although close in magnitude, it does not preserve the uniform increment required in an arithmetic progression. Hence, it cannot be accepted as the next term.

Option D:
Option D, 16, would represent an even larger jump of 5, again contradicting the constant difference already established. Such a change would introduce a new pattern not supported by the original data, so it is not appropriate.