Identify the sequence as arithmetic. geometric, or neither.. explain your answer
1.6, 0.8, 0.4, 0.2
Did you notice that each term is half of the previous one?
Which type of sequence matches that property?
To identify the given sequence as arithmetic, geometric, or neither, we need to analyze the pattern and calculate the common difference or common ratio between the terms.
In an arithmetic sequence, the difference between consecutive terms is constant. To check if the given sequence is arithmetic, we subtract each term from its consecutive term. Let's do that:
0.8 - 1.6 = -0.8
0.4 - 0.8 = -0.4
0.2 - 0.4 = -0.2
As you can see, the differences are not constant. In an arithmetic sequence, we would expect the differences to be the same. Therefore, we can conclude that the given sequence is not arithmetic.
Now, let's check if the given sequence is geometric. In a geometric sequence, each term is a product of the previous term and a common ratio. To check if the given sequence is geometric, we divide each term by its preceding term. Let's do that:
0.8 / 1.6 = 0.5
0.4 / 0.8 = 0.5
0.2 / 0.4 = 0.5
As you can observe, each division yields the same result, which is 0.5. This indicates that there is a common ratio of 0.5 between each term. Since the ratio is constant, we can conclude that the given sequence is geometric.
In summary, the given sequence 1.6, 0.8, 0.4, 0.2 is a geometric sequence with a common ratio of 0.5.