Identify the sequence as arithmetic. geometric, or neither.. explain your answer
1.6, 0.8, 0.4, 0.2....
0.8 / 1.6 = 0.5
0.4 / 0.8 = 0.5
0.2 / 0.4 = 0.5
Geometric progression with common ratio
q =0 .5
–2, –0.8, 0.4, 1.6,
The given sequence 1.6, 0.8, 0.4, 0.2... is a geometric sequence.
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant factor called the common ratio. In this sequence, each term is obtained by dividing the previous term by 2, so the common ratio is 1/2.
To verify this, let's check if each term is obtained by multiplying the previous term by the common ratio:
0.8 = 1.6 * (1/2)
0.4 = 0.8 * (1/2)
0.2 = 0.4 * (1/2)
As we can see, each term is indeed the result of multiplying the previous term by 1/2. Therefore, the given sequence is a geometric sequence.
To determine whether the sequence 1.6, 0.8, 0.4, 0.2... is arithmetic, geometric, or neither, we need to understand the characteristics of each type of sequence.
1. Arithmetic sequence: In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. For example, in the sequence 1, 4, 7, 10, the constant difference is 3.
2. Geometric sequence: In a geometric sequence, each term is obtained by multiplying a constant ratio to the previous term. For example, in the sequence 2, 4, 8, 16, the constant ratio is 2.
Now, let's analyze the given sequence 1.6, 0.8, 0.4, 0.2...
First, let's calculate the ratios between consecutive terms:
0.8 ÷ 1.6 = 0.5
0.4 ÷ 0.8 = 0.5
0.2 ÷ 0.4 = 0.5
Since each ratio between consecutive terms is the same (0.5), the sequence has a constant ratio. Therefore, this sequence is a geometric sequence.
To summarize, the sequence 1.6, 0.8, 0.4, 0.2... is a geometric sequence because each term is obtained by multiplying a constant ratio (0.5) to the previous term.