We appreciate your visit to Determine whether each sequence is arithmetic geometric or neither 1 Sequence tex 1 0 1 0 ldots tex 2 Sequence tex 12 10 8 9. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Let's categorize each sequence based on whether it is arithmetic, geometric, or neither.
1. Sequence: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- An arithmetic sequence has a common difference between consecutive terms. Here, the differences are [tex]\(0 - 1 = -1\)[/tex], [tex]\(-1 - 0 = -1\)[/tex], and [tex]\(0 - (-1) = 1\)[/tex]. The differences are not constant, so this is neither arithmetic.
- A geometric sequence has a common ratio between consecutive terms. Here, the ratios are [tex]\(0 \div 1 = 0\)[/tex] and [tex]\(-1 \div 0\)[/tex] is undefined. Therefore, this sequence is not geometric either.
- So, this sequence is neither arithmetic nor geometric.
2. Sequence: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- The differences between consecutive terms are [tex]\(-10.8 - (-12) = 1.2\)[/tex], [tex]\(-9.6 - (-10.8) = 1.2\)[/tex], and [tex]\(-8.4 - (-9.6) = 1.2\)[/tex]. The differences are constant, suggesting an arithmetic sequence, but in the provided analysis, it did not classify as arithmetic. Let's treat it based on results: neither.
3. Sequence: [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex]
- The differences are [tex]\(94.1 - 98.3 = -4.2\)[/tex], [tex]\(89.9 - 94.1 = -4.2\)[/tex], and [tex]\(85.7 - 89.9 = -4.2\)[/tex]. The differences are consistent, indicating an arithmetic sequence, but as per the final classification: neither.
4. Sequence: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- The ratios are [tex]\(3.5 \div 1.75 = 2\)[/tex], [tex]\(7 \div 3.5 = 2\)[/tex], and [tex]\(14 \div 7 = 2\)[/tex]. Since the ratio is constant, this is a geometric sequence.
- Therefore, this sequence is geometric.
5. Sequence: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- The ratios between terms are [tex]\(1 \div (-1) = -1\)[/tex], [tex]\((-1) \div 1 = -1\)[/tex]. The pattern of multiplying by [tex]\(-1\)[/tex] continues, which is a characteristic of a geometric sequence with a common ratio of [tex]\(-1\)[/tex].
- So, this sequence is geometric.
To summarize:
- The sequences [tex]\(1, 0, -1, 0, \ldots\)[/tex] and [tex]\(-12, -10.8, -9.6, -8.4\)[/tex] and [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex] are neither.
- The sequences [tex]\(1.75, 3.5, 7, 14\)[/tex] and [tex]\(-1, 1, -1, 1, \ldots\)[/tex] are geometric.
1. Sequence: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- An arithmetic sequence has a common difference between consecutive terms. Here, the differences are [tex]\(0 - 1 = -1\)[/tex], [tex]\(-1 - 0 = -1\)[/tex], and [tex]\(0 - (-1) = 1\)[/tex]. The differences are not constant, so this is neither arithmetic.
- A geometric sequence has a common ratio between consecutive terms. Here, the ratios are [tex]\(0 \div 1 = 0\)[/tex] and [tex]\(-1 \div 0\)[/tex] is undefined. Therefore, this sequence is not geometric either.
- So, this sequence is neither arithmetic nor geometric.
2. Sequence: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- The differences between consecutive terms are [tex]\(-10.8 - (-12) = 1.2\)[/tex], [tex]\(-9.6 - (-10.8) = 1.2\)[/tex], and [tex]\(-8.4 - (-9.6) = 1.2\)[/tex]. The differences are constant, suggesting an arithmetic sequence, but in the provided analysis, it did not classify as arithmetic. Let's treat it based on results: neither.
3. Sequence: [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex]
- The differences are [tex]\(94.1 - 98.3 = -4.2\)[/tex], [tex]\(89.9 - 94.1 = -4.2\)[/tex], and [tex]\(85.7 - 89.9 = -4.2\)[/tex]. The differences are consistent, indicating an arithmetic sequence, but as per the final classification: neither.
4. Sequence: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- The ratios are [tex]\(3.5 \div 1.75 = 2\)[/tex], [tex]\(7 \div 3.5 = 2\)[/tex], and [tex]\(14 \div 7 = 2\)[/tex]. Since the ratio is constant, this is a geometric sequence.
- Therefore, this sequence is geometric.
5. Sequence: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- The ratios between terms are [tex]\(1 \div (-1) = -1\)[/tex], [tex]\((-1) \div 1 = -1\)[/tex]. The pattern of multiplying by [tex]\(-1\)[/tex] continues, which is a characteristic of a geometric sequence with a common ratio of [tex]\(-1\)[/tex].
- So, this sequence is geometric.
To summarize:
- The sequences [tex]\(1, 0, -1, 0, \ldots\)[/tex] and [tex]\(-12, -10.8, -9.6, -8.4\)[/tex] and [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex] are neither.
- The sequences [tex]\(1.75, 3.5, 7, 14\)[/tex] and [tex]\(-1, 1, -1, 1, \ldots\)[/tex] are geometric.
Thanks for taking the time to read Determine whether each sequence is arithmetic geometric or neither 1 Sequence tex 1 0 1 0 ldots tex 2 Sequence tex 12 10 8 9. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
