Is the following sequence a arithmetic,geometric or neither?
1.6, .8, .4, .2
my answer is geometric
Right
To determine if a sequence is arithmetic, geometric, or neither, we need to check if there is a consistent pattern between the terms.
In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. For example, the sequence 1, 3, 5, 7 is arithmetic because each term is obtained by adding 2 to the previous term.
In a geometric sequence, each term is obtained by multiplying a constant ratio to the previous term. For example, the sequence 2, 6, 18, 54 is geometric because each term is obtained by multiplying 3 to the previous term.
Let's analyze the given sequence: 1.6, 0.8, 0.4, 0.2.
To determine if it is arithmetic, we would check if there is a consistent difference between the terms. However, there is no constant difference between the terms.
To determine if it is geometric, we would check if there is a consistent ratio between the terms. By dividing any term by the previous term, we can determine if a common ratio exists.
Dividing 0.8 by 1.6 gives 0.5.
Dividing 0.4 by 0.8 gives 0.5.
Dividing 0.2 by 0.4 gives 0.5.
Since there is a consistent ratio of 0.5 between each term, we can conclude that the given sequence is indeed geometric.