Identify the sequence as arithmetic, geometric, or neither. Explain your answer 1.6, 0.8, 0.4, 0.2
This is a geometric sequence because the ratio between each term is constant (1/2).
To determine whether the given sequence is arithmetic, geometric, or neither, we need to examine the common difference or ratio between the terms.
If there is a constant difference between consecutive terms, the sequence is arithmetic. If there is a constant ratio between consecutive terms, the sequence is geometric. If neither the difference nor the ratio is constant, then the sequence is neither arithmetic nor geometric.
Let's examine the given sequence: 1.6, 0.8, 0.4, 0.2
To find the common ratio or difference, we can divide any term by its preceding term:
0.8/1.6 = 0.5
0.4/0.8 = 0.5
0.2/0.4 = 0.5
Since the ratio between all consecutive terms in the given sequence is constant (0.5), we can conclude that the sequence is geometric.
Explanation: The given sequence is geometric because the ratio between each term and its preceding term is constant, specifically, 0.5.
To identify whether a sequence is arithmetic, geometric, or neither, we need to analyze the pattern between the terms.
In an arithmetic sequence, there is a common difference between each pair of consecutive terms. To check if the given sequence is arithmetic, we need to see if the difference between any two consecutive terms is constant.
Let's calculate the differences between the terms:
0.8 - 1.6 = -0.8
0.4 - 0.8 = -0.4
0.2 - 0.4 = -0.2
As we can see, the differences are not constant. The first difference is -0.8, the second difference is -0.4, and the third difference is -0.2. This confirms that the given sequence is not arithmetic.
Now, let's analyze if the sequence is geometric. In a geometric sequence, there is a common ratio between each pair of consecutive terms. To determine if the given sequence is geometric, we need to check if the ratio between any two consecutive terms is constant.
Let's calculate the ratios between the terms:
0.8 / 1.6 = 0.5
0.4 / 0.8 = 0.5
0.2 / 0.4 = 0.5
As we can see, the ratios between the terms are all equal to 0.5. This confirms that the given sequence is geometric.
Therefore, the sequence 1.6, 0.8, 0.4, 0.2 is a geometric sequence, with a common ratio of 0.5.