Identify the sequence as arithmetic, geometric, or neither. Explain your answer.
1.6, 0.8, 0.4, 0.2,...
It's geometric
each term is half of the previous term
Is it a arithmetic, geometric or neither?
To identify whether a sequence is arithmetic, geometric, or neither, we need to look for patterns in the differences or ratios between consecutive terms.
In the given sequence 1.6, 0.8, 0.4, 0.2,..., let's start by finding the differences between consecutive terms:
0.8 - 1.6 = -0.8
0.4 - 0.8 = -0.4
0.2 - 0.4 = -0.2
From this, we can see that the differences are all negative and are also decreasing by a factor of 0.2 each time.
Next, let's find the ratios between consecutive terms:
0.8 / 1.6 = 0.5
0.4 / 0.8 = 0.5
0.2 / 0.4 = 0.5
From this, we can see that the ratios between consecutive terms are all 0.5, which is a constant value.
Based on these observations, we can conclude that the given sequence is a geometric sequence because the ratios between consecutive terms are constant. In this case, the common ratio is 0.5.