Identify the sequence as arithmetic geometric or neither
1.6,0.8,0.4,0.2…..
The given sequence is a geometric sequence because the ratio between any two consecutive terms is the same. In this case, dividing any term by the previous term, we get:
0.8/1.6 = 0.5
0.4/0.8 = 0.5
0.2/0.4 = 0.5
So, the common ratio between any two consecutive terms is 0.5.
nerd
To identify if the sequence 1.6, 0.8, 0.4, 0.2... is arithmetic or geometric, we need to check if there is a common difference or a common ratio between the terms.
1. To check if it's an arithmetic sequence, we subtract each term from its previous term to see if we get a constant difference:
0.8 - 1.6 = -0.8
0.4 - 0.8 = -0.4
0.2 - 0.4 = -0.2
Since the differences are not constant, the sequence is not arithmetic.
2. To check if it's a geometric sequence, we divide each term by its previous term to check if there is a constant ratio:
0.8 / 1.6 = 0.5
0.4 / 0.8 = 0.5
0.2 / 0.4 = 0.5
Since the ratios are constant (0.5), the sequence is geometric.
Therefore, the sequence 1.6, 0.8, 0.4, 0.2... is a geometric sequence.
To identify the sequence as arithmetic, geometric, or neither, we need to look for a consistent pattern in the terms of the sequence.
First, let's calculate the common difference 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 between consecutive terms are not the same. In an arithmetic sequence, the differences between consecutive terms are constant. Since the differences in this sequence are not constant, we can conclude that it is not an arithmetic sequence.
Now let's calculate the common ratio between the terms:
0.8 ÷ 1.6 = 0.5
0.4 ÷ 0.8 = 0.5
0.2 ÷ 0.4 = 0.5
Here, we can see that the ratio between consecutive terms is the same: 0.5. In a geometric sequence, the ratio between consecutive terms is constant. Since the ratio in this sequence is constant, we can conclude that it is a geometric sequence.
Therefore, the given sequence 1.6, 0.8, 0.4, 0.2... is a geometric sequence.