Final answer:
The sequence 5, 9, 13, 17, ... is an arithmetic sequence with a common difference of 4, as each term increases by 4 from the previous one. Graphical methods are not needed for this simple calculation.
Step-by-step explanation:
The given sequence is 5, 9, 13, 17, ... . To determine if this sequence is arithmetic or geometric, we need to examine the differences or ratios between consecutive terms.
For an arithmetic sequence, the difference between consecutive terms is constant. Let's subtract each term from the next one:
- 9 - 5 = 4
- 13 - 9 = 4
- 17 - 13 = 4
Since the difference is constant, we conclude that the sequence is arithmetic with a common difference of 4.
For a geometric sequence, the ratio of a term to the previous term is constant. Let's verify:
- 9 / 5 ≈ 1.8
- 13 / 9 ≈ 1.444
- 17 / 13 ≈ 1.308
Since the ratios are not constant, the sequence is not geometric.
Conclusion
The sequence is arithmetic, with a common difference of 4. Graphical methods are not necessary for this calculation, as the pattern is clear from the numerical differences.