Question
arithmetic or geometric
-10,-8,-6,-4,...
-10,-8,-6,-4,...
Answers
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Answered by
GPT-4o mini
The sequence you've provided is \(-10, -8, -6, -4, \ldots\).
To determine whether it is an arithmetic or geometric sequence, we can look at the differences and ratios between the terms:
1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant.
Let's find the difference:
- \(-8 - (-10) = -8 + 10 = 2\)
- \(-6 - (-8) = -6 + 8 = 2\)
- \(-4 - (-6) = -4 + 6 = 2\)
The difference is consistently \(2\).
2. **Geometric Sequence**: In a geometric sequence, the ratio between consecutive terms is constant.
Let's find the ratios:
- \(-8 / -10 = 0.8\)
- \(-6 / -8 = 0.75\)
- \(-4 / -6 = \frac{2}{3}\)
The ratios are not constant.
Since the differences between consecutive terms are constant and the ratios are not, the sequence \(-10, -8, -6, -4, \ldots\) is an **arithmetic sequence** with a common difference of \(2\).
To determine whether it is an arithmetic or geometric sequence, we can look at the differences and ratios between the terms:
1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant.
Let's find the difference:
- \(-8 - (-10) = -8 + 10 = 2\)
- \(-6 - (-8) = -6 + 8 = 2\)
- \(-4 - (-6) = -4 + 6 = 2\)
The difference is consistently \(2\).
2. **Geometric Sequence**: In a geometric sequence, the ratio between consecutive terms is constant.
Let's find the ratios:
- \(-8 / -10 = 0.8\)
- \(-6 / -8 = 0.75\)
- \(-4 / -6 = \frac{2}{3}\)
The ratios are not constant.
Since the differences between consecutive terms are constant and the ratios are not, the sequence \(-10, -8, -6, -4, \ldots\) is an **arithmetic sequence** with a common difference of \(2\).
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