Final answer:
The sequence -13, -26, -39, -52,... is an arithmetic sequence because it has a common difference of -13 between each successive term.
Step-by-step explanation:
To determine whether the sequence -13, -26, -39, -52,... is arithmetic or geometric, we need to look at the differences or ratios between successive terms. An arithmetic sequence has a common difference between each term, while a geometric sequence has a common ratio.
To find out, we calculate:
- Difference between the second and the first term: -26 - (-13) = -13
- Difference between the third and the second term: -39 - (-26) = -13
- Difference between the fourth and the third term: -52 - (-39) = -13
Since the difference is consistent and equals -13 for each pair of successive terms, we can conclude that the sequence is an arithmetic sequence with a common difference of -13.