identify the sequence as arithmetic, geometric, or neither. please explain answer
1.6,0.8, 0.4, 0.2,...
1.6 * 0.5 = 0.8
0.8 * 0.5 = 0.4
0.4 * 0.5 = 0.2
What do you think that is?
i don't know i need help
In a Geometric Sequence each term is found by multiplying the previous term by a constant.
In this case constant = 0.5
Geometric Sequence
To identify if the given sequence is arithmetic, geometric, or neither, we need to understand the characteristics of each type of sequence.
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. In other words, if you subtract any term from the following term, you will always get the same value.
A geometric sequence, on the other hand, is a sequence in which the ratio between any two consecutive terms is constant. In other words, if you divide any term by the previous term, you will always get the same value.
Now let's analyze the given sequence: 1.6, 0.8, 0.4, 0.2,...
To determine if it is arithmetic, we need to check if the differences between consecutive terms are constant:
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, meaning it is not an arithmetic sequence.
Next, let's determine if it is geometric by checking if the ratios between consecutive terms are constant:
0.8 / 1.6 = 0.5
0.4 / 0.8 = 0.5
0.2 / 0.4 = 0.5
The ratios between consecutive terms are indeed constant (0.5), which means the given sequence is a geometric sequence.
To summarize:
- The given sequence 1.6, 0.8, 0.4, 0.2, ... is geometric.
- The ratio between consecutive terms is 0.5.
Therefore, the sequence is a geometric sequence.