UGC NET Questions (Paper – 1)

The given sequence increases from 5 to 9, from 9 to 13, and from 13 to 17. In each step, the increase is 4, which means the common difference is 4. Such a sequence with constant difference is an example of an arithmetic progression. Therefore, adding 4 each time correctly describes the pattern generating the sequence.

Option A:
The option 4 is correct because 9−5, 13−9 and 17−13 all equal 4. In arithmetic progression questions, identifying the constant difference is the key step to predicting the next term. If we add 4 to 17, we get 21 as the next term, which fits the discovered pattern. Hence, 4 is the only value that maintains the same step throughout the sequence.

Option B:
Adding 5 each time would give 5, 10, 15, 20, which is not the given sequence. The actual terms 9, 13 and 17 would not be obtained by repeated addition of 5 starting from 5. This shows that 5 does not match the observed pattern. So, this option is incorrect.

Option C:
Adding 3 at each step would produce 5, 8, 11, 14 and so on, which again does not coincide with the given terms 9, 13 and 17. The difference between each pair of consecutive terms is clearly 4, not 3. Therefore, this option does not fit the sequence.

Option D:
Adding 2 each time gives the series 5, 7, 9, 11, which is different from the one given in the question. Although 2 is a possible constant difference in other series, it cannot describe the pattern here because the actual increments are larger. Hence, this option must be rejected.

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.

A and B define AP and GP. D is true because the sign of the common difference determines whether an AP increases, decreases, or stays constant. E is true because multiplying by −1 flips a non-zero term’s sign each step, alternating between a and −a. C is false (Fibonacci-type recurrence is generally neither AP nor GP). Hence A, B, D and E only are correct.

Option A:
Option A is incomplete as it omits E, a standard GP special case often tested.

Option B:
Option B is correct because it combines the core definitions with typical behaviour of APs and a specific GP example, and excludes C, which is false.

Option C:
Option C is wrong because it omits A, the definition of an arithmetic sequence.

Option D:
Option D is incorrect because it omits B, the definition of a geometric sequence.

Statements A, B and C provide the definition, nth term and sum formula for APs. Statement D is also correct because terms equidistant from the ends have the same average (equal to the average of first and last). Statement E is false since d = 0 gives a constant sequence, which is still an AP. Thus A, B, C and D only are correct.

Option A:
Option A is incomplete as it omits D (symmetry property).

Option B:
Option B is incomplete because it omits B (nth term formula), so it misses a core true statement.

Option C:
Option C is incomplete since it omits A (definition), so it does not include the full true set.

Option D:
Option D is correct because it unites all true statements and excludes E (false).

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.