identify the sequence 1.6, .8, .4, .2 as arithmetic, geometric, or neither and why.
To determine whether the sequence 1.6, 0.8, 0.4, 0.2 is arithmetic, geometric, or neither, let's examine the differences between consecutive terms:
0.8 - 1.6 = -0.8
0.4 - 0.8 = -0.4
0.2 - 0.4 = -0.2
Since the differences between terms are not constant, the sequence is not arithmetic.
Next, let's examine 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 between consecutive terms are constant (0.5), which implies that the sequence is geometric.
Therefore, the sequence 1.6, 0.8, 0.4, 0.2 is a geometric sequence because the ratios between consecutive terms are constant.
To identify whether the sequence 1.6, 0.8, 0.4, 0.2 is arithmetic, geometric, or neither, we need to observe the pattern between consecutive terms.
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is always the same. In other words, if we subtract any term from the next term, we should get a constant difference.
For example, in the arithmetic sequence 2, 4, 6, 8, 10, the difference between any two consecutive terms is always 2.
A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a constant ratio. In other words, if we divide any term by its previous term, we should get a constant value.
For example, in the geometric sequence 2, 4, 8, 16, 32, the ratio between any two consecutive terms is always 2.
Let's check the given sequence:
1.6 / 0.8 = 2
0.8 / 0.4 = 2
0.4 / 0.2 = 2
Since the ratio between any two consecutive terms is always 2, we can conclude that the given sequence is a geometric sequence. Each term is obtained by dividing the previous term by 2.