Identify the sequence as arithmetic, geometric, or neither. Explain your answer. 1.6, 0.8, 0.4, 0.2 . . .
.8/1.6 = .5
.4/.8 = .5
.2/.4 = .5
Constant
Geometric
To determine whether the given sequence is arithmetic, geometric, or neither, we need to examine the pattern of the terms.
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant.
A geometric sequence is a sequence in which the ratio between any two consecutive terms is constant.
Let's calculate the differences and ratios between the terms:
Difference between 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.
Ratio between terms:
0.8 / 1.6 = 0.5
0.4 / 0.8 = 0.5
0.2 / 0.4 = 0.5
The ratios are constant (0.5), so the sequence is geometric.
Thus, the given sequence is geometric because the ratio between any two consecutive terms, 0.5, is constant.