We appreciate your visit to Classify the sequences according to whether they are arithmetic geometric or neither 1 tex 1 0 1 0 ldots tex 2 tex 1 75 3. 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 analyze each sequence one by one.
1. For the sequence
[tex]$$
1,\;0,\;-1,\;0,\;\ldots
$$[/tex]
• To see if it is arithmetic, we compute the differences between consecutive terms:
[tex]$$
0 - 1 = -1,\quad -1 - 0 = -1,\quad 0 - (-1) = 1.
$$[/tex]
The differences are not constant (we have both [tex]\(-1\)[/tex] and [tex]\(1\)[/tex]).
• To see if it is geometric, we look at the ratios. However, since one of the terms is [tex]\(0\)[/tex], the ratio is not defined for all steps.
Therefore, this sequence is neither arithmetic nor geometric.
2. For the sequence
[tex]$$
1.75,\;3.5,\;7,\;14
$$[/tex]
• We check if it is geometric by computing the ratios:
[tex]$$
\frac{3.5}{1.75} = 2,\quad \frac{7}{3.5} = 2,\quad \frac{14}{7} = 2.
$$[/tex]
Since the ratio is constant ([tex]\(2\)[/tex]), the sequence is geometric.
3. For the sequence
[tex]$$
-12,\;-10.8,\;-9.6,\;-8.4
$$[/tex]
• We check if it is arithmetic by computing the differences:
[tex]$$
-10.8 - (-12) = 1.2,\quad -9.6 - (-10.8) = 1.2,\quad -8.4 - (-9.6) = 1.2.
$$[/tex]
The constant difference [tex]\(1.2\)[/tex] shows that this sequence is arithmetic.
4. For the sequence
[tex]$$
98.3,\;94.1,\;89.9,\;85.7
$$[/tex]
• Compute the differences:
[tex]$$
94.1 - 98.3 = -4.2,\quad 89.9 - 94.1 = -4.2,\quad 85.7 - 89.9 = -4.2.
$$[/tex]
All differences are the same ([tex]\(-4.2\)[/tex]), so this sequence is arithmetic.
5. For the sequence
[tex]$$
-1,\;1,\;-1,\;1,\;\ldots
$$[/tex]
• We check if it is geometric by computing the ratios:
[tex]$$
\frac{1}{-1} = -1,\quad \frac{-1}{1} = -1.
$$[/tex]
The common ratio is [tex]\(-1\)[/tex], so the sequence is geometric.
Thus, the final classifications are:
- Sequence 1: Neither
- Sequence 2: Geometric
- Sequence 3: Arithmetic
- Sequence 4: Arithmetic
- Sequence 5: Geometric
1. For the sequence
[tex]$$
1,\;0,\;-1,\;0,\;\ldots
$$[/tex]
• To see if it is arithmetic, we compute the differences between consecutive terms:
[tex]$$
0 - 1 = -1,\quad -1 - 0 = -1,\quad 0 - (-1) = 1.
$$[/tex]
The differences are not constant (we have both [tex]\(-1\)[/tex] and [tex]\(1\)[/tex]).
• To see if it is geometric, we look at the ratios. However, since one of the terms is [tex]\(0\)[/tex], the ratio is not defined for all steps.
Therefore, this sequence is neither arithmetic nor geometric.
2. For the sequence
[tex]$$
1.75,\;3.5,\;7,\;14
$$[/tex]
• We check if it is geometric by computing the ratios:
[tex]$$
\frac{3.5}{1.75} = 2,\quad \frac{7}{3.5} = 2,\quad \frac{14}{7} = 2.
$$[/tex]
Since the ratio is constant ([tex]\(2\)[/tex]), the sequence is geometric.
3. For the sequence
[tex]$$
-12,\;-10.8,\;-9.6,\;-8.4
$$[/tex]
• We check if it is arithmetic by computing the differences:
[tex]$$
-10.8 - (-12) = 1.2,\quad -9.6 - (-10.8) = 1.2,\quad -8.4 - (-9.6) = 1.2.
$$[/tex]
The constant difference [tex]\(1.2\)[/tex] shows that this sequence is arithmetic.
4. For the sequence
[tex]$$
98.3,\;94.1,\;89.9,\;85.7
$$[/tex]
• Compute the differences:
[tex]$$
94.1 - 98.3 = -4.2,\quad 89.9 - 94.1 = -4.2,\quad 85.7 - 89.9 = -4.2.
$$[/tex]
All differences are the same ([tex]\(-4.2\)[/tex]), so this sequence is arithmetic.
5. For the sequence
[tex]$$
-1,\;1,\;-1,\;1,\;\ldots
$$[/tex]
• We check if it is geometric by computing the ratios:
[tex]$$
\frac{1}{-1} = -1,\quad \frac{-1}{1} = -1.
$$[/tex]
The common ratio is [tex]\(-1\)[/tex], so the sequence is geometric.
Thus, the final classifications are:
- Sequence 1: Neither
- Sequence 2: Geometric
- Sequence 3: Arithmetic
- Sequence 4: Arithmetic
- Sequence 5: Geometric
Thanks for taking the time to read Classify the sequences according to whether they are arithmetic geometric or neither 1 tex 1 0 1 0 ldots tex 2 tex 1 75 3. 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
