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9. Identify the sequence as arithmetic, geometric, or neither. Explain your answer.
1.6, 0.8, 0.4, 0.2, . . .
no common difference
common ratio is 0.5, so ...
To identify the sequence as arithmetic, geometric, or neither, let's first understand the characteristics of each type of sequence:
1. Arithmetic sequence: In an arithmetic sequence, each term is obtained by adding a common difference (d) to the previous term. For example, the sequence 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.
2. Geometric sequence: In a geometric sequence, each term is obtained by multiplying a common ratio (r) to the previous term. For example, the sequence 2, 6, 18, 54 is a geometric sequence with a common ratio of 3.
Now, let's analyze the given sequence: 1.6, 0.8, 0.4, 0.2, ...
Looking at the terms, we can notice that each term is obtained by dividing the previous term by 2. For example, 1.6 ÷ 2 = 0.8, 0.8 ÷ 2 = 0.4, 0.4 ÷ 2 = 0.2, and so on.
Since each term is obtained by dividing the previous term by 2, we can conclude that the given sequence is a geometric sequence with a common ratio of 1/2.
Therefore, the answer is: The sequence 1.6, 0.8, 0.4, 0.2, ... is a geometric sequence.