identify the sequence as arithmetic, geometric, or neither. explain your answer.

1.6 , 0.8 , 0.4 , 0.2 ....

It looks like we are taking 1/2 of the previous number or dividing by two. Any time you are multiplying or dividing you have a geometric sequence. If you are adding or subtracting a constant, then you have an arithmetic sequence.

geometric... just common sense

Why is it Geometric though

To identify whether the given sequence is arithmetic, geometric, or neither, we need to examine the pattern and behavior of the numbers in the sequence.

For an arithmetic sequence, each term is obtained by adding or subtracting a constant value called the "common difference" to the previous term. In other words, the difference between any two consecutive terms is constant.

For a geometric sequence, each term is obtained by multiplying or dividing a constant value called the "common ratio" with the previous term. In other words, the ratio of any two consecutive terms is constant.

Now, let's examine the given sequence: 1.6, 0.8, 0.4, 0.2, ...

To determine if it is an arithmetic sequence, we will check the differences between consecutive terms:

0.8 - 1.6 = -0.8
0.4 - 0.8 = -0.4
0.2 - 0.4 = -0.2

The differences are not constant, so the sequence is not arithmetic.

To determine if it is a geometric sequence, we will check the ratios between consecutive terms:

0.8 / 1.6 = 0.5
0.4 / 0.8 = 0.5
0.2 / 0.4 = 0.5

The ratios are constant, with a common ratio of 0.5. Therefore, the given sequence is a geometric sequence.

In conclusion, the given sequence, 1.6, 0.8, 0.4, 0.2, ... is a geometric sequence because there is a constant common ratio of 0.5 between consecutive terms.