Constant difference in number series – UGC NET Question

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.