Final answer:
The sequence is a geometric sequence with a common ratio of -(2/3), identified by dividing each term by the previous term and finding a constant ratio.
Step-by-step explanation:
To determine if the sequence is arithmetic or geometric, we should look at the pattern of the terms in the sequence. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms. Let's choose three consecutive terms to analyze: -(10/3), (20/9), and -(40/27).
- For an arithmetic sequence, we would expect each term to be obtained by adding a fixed number to the previous term.
- For a geometric sequence, each term is obtained by multiplying the previous term by a fixed number.
Let's check for a constant ratio by dividing each term by the previous term:
- (20/9) ÷ (-(10/3)) = -(20/9) * (-(3/10)) = (60/90) = (2/3)
- -(40/27) ÷ (20/9) = -(40/27) * (9/20) = -(360/540) = -(2/3)
Notice that when we divide each term by the previous term, we get the same ratio of -(2/3). This indicates that the sequence is indeed a geometric sequence with a common ratio of -(2/3).