At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Let's thoroughly analyze each sequence to determine which one is an arithmetic sequence. An arithmetic sequence is one in which the difference between consecutive terms is constant.
Sequence A: [tex]\(1, 1, 2, 3, 5, 8, \ldots\)[/tex]
To check if this sequence is arithmetic, let's compute the differences between consecutive terms:
- [tex]\(1 - 1 = 0\)[/tex]
- [tex]\(2 - 1 = 1\)[/tex]
- [tex]\(3 - 2 = 1\)[/tex]
- [tex]\(5 - 3 = 2\)[/tex]
- [tex]\(8 - 5 = 3\)[/tex]
The differences are [tex]\(0, 1, 1, 2, 3\)[/tex], which are not constant. Therefore, Sequence A is not an arithmetic sequence.
Sequence B: [tex]\(-2, 3, 8, 13, 18, \ldots\)[/tex]
Now let's compute the differences between consecutive terms for this sequence:
- [tex]\(3 - (-2) = 5\)[/tex]
- [tex]\(8 - 3 = 5\)[/tex]
- [tex]\(13 - 8 = 5\)[/tex]
- [tex]\(18 - 13 = 5\)[/tex]
The differences are [tex]\(5, 5, 5, 5\)[/tex], which are constant. Therefore, Sequence B is an arithmetic sequence.
Sequence C: [tex]\(1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \ldots\)[/tex]
Let's compute the differences between consecutive terms:
- [tex]\(\frac{1}{2} - 1 = -\frac{1}{2}\)[/tex]
- [tex]\(\frac{1}{4} - \frac{1}{2} = -\frac{1}{4}\)[/tex]
- [tex]\(\frac{1}{8} - \frac{1}{4} = -\frac{1}{8}\)[/tex]
The differences are [tex]\(-\frac{1}{2}, -\frac{1}{4}, -\frac{1}{8}\)[/tex], which are not constant. Therefore, Sequence C is not an arithmetic sequence.
Sequence D: [tex]\(4, -4, 4, -4, 4, \ldots\)[/tex]
Let's compute the differences between consecutive terms:
- [tex]\(-4 - 4 = -8\)[/tex]
- [tex]\(4 - (-4) = 8\)[/tex]
- [tex]\(-4 - 4 = -8\)[/tex]
- [tex]\(4 - (-4) = 8\)[/tex]
The differences are [tex]\(-8, 8, -8, 8\)[/tex], which are not constant. Therefore, Sequence D is not an arithmetic sequence.
Given the detailed analysis, the only arithmetic sequence is:
B. [tex]\(-2, 3, 8, 13, 18, \ldots\)[/tex]
Thus, the correct choice is [tex]\( \boxed{2} \)[/tex].
Sequence A: [tex]\(1, 1, 2, 3, 5, 8, \ldots\)[/tex]
To check if this sequence is arithmetic, let's compute the differences between consecutive terms:
- [tex]\(1 - 1 = 0\)[/tex]
- [tex]\(2 - 1 = 1\)[/tex]
- [tex]\(3 - 2 = 1\)[/tex]
- [tex]\(5 - 3 = 2\)[/tex]
- [tex]\(8 - 5 = 3\)[/tex]
The differences are [tex]\(0, 1, 1, 2, 3\)[/tex], which are not constant. Therefore, Sequence A is not an arithmetic sequence.
Sequence B: [tex]\(-2, 3, 8, 13, 18, \ldots\)[/tex]
Now let's compute the differences between consecutive terms for this sequence:
- [tex]\(3 - (-2) = 5\)[/tex]
- [tex]\(8 - 3 = 5\)[/tex]
- [tex]\(13 - 8 = 5\)[/tex]
- [tex]\(18 - 13 = 5\)[/tex]
The differences are [tex]\(5, 5, 5, 5\)[/tex], which are constant. Therefore, Sequence B is an arithmetic sequence.
Sequence C: [tex]\(1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \ldots\)[/tex]
Let's compute the differences between consecutive terms:
- [tex]\(\frac{1}{2} - 1 = -\frac{1}{2}\)[/tex]
- [tex]\(\frac{1}{4} - \frac{1}{2} = -\frac{1}{4}\)[/tex]
- [tex]\(\frac{1}{8} - \frac{1}{4} = -\frac{1}{8}\)[/tex]
The differences are [tex]\(-\frac{1}{2}, -\frac{1}{4}, -\frac{1}{8}\)[/tex], which are not constant. Therefore, Sequence C is not an arithmetic sequence.
Sequence D: [tex]\(4, -4, 4, -4, 4, \ldots\)[/tex]
Let's compute the differences between consecutive terms:
- [tex]\(-4 - 4 = -8\)[/tex]
- [tex]\(4 - (-4) = 8\)[/tex]
- [tex]\(-4 - 4 = -8\)[/tex]
- [tex]\(4 - (-4) = 8\)[/tex]
The differences are [tex]\(-8, 8, -8, 8\)[/tex], which are not constant. Therefore, Sequence D is not an arithmetic sequence.
Given the detailed analysis, the only arithmetic sequence is:
B. [tex]\(-2, 3, 8, 13, 18, \ldots\)[/tex]
Thus, the correct choice is [tex]\( \boxed{2} \)[/tex].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
