At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine which of the given sequences is an arithmetic sequence, we need to check if the differences between consecutive terms are consistent.
An arithmetic sequence is one in which the difference between any two consecutive terms is constant. This difference is known as the common difference.
Let's analyze each sequence step-by-step:
1. Sequence: [tex]\(\{724, -362, 181, -90.5\}\)[/tex]
- Difference between the first and second terms: [tex]\(-362 - 724 = -1086\)[/tex]
- Difference between the second and third terms: [tex]\(181 - (-362) = 181 + 362 = 543\)[/tex]
- Difference between the third and fourth terms: [tex]\(-90.5 - 181 = -271.5\)[/tex]
Since the differences are [tex]\(-1086\)[/tex], [tex]\(543\)[/tex], and [tex]\(-271.5\)[/tex] which are not consistent, this sequence is not arithmetic.
2. Sequence: [tex]\(\{232, 354, 476, 598, \ldots\}\)[/tex]
- Difference between the first and second terms: [tex]\(354 - 232 = 122\)[/tex]
- Difference between the second and third terms: [tex]\(476 - 354 = 122\)[/tex]
- Difference between the third and fourth terms: [tex]\(598 - 476 = 122\)[/tex]
Since the differences are [tex]\(122\)[/tex], [tex]\(122\)[/tex], and [tex]\(122\)[/tex] which are consistent, this sequence is arithmetic with a common difference of [tex]\(122\)[/tex].
3. Sequence: [tex]\(\{691, 632, 573, 514\}\)[/tex]
- Difference between the first and second terms: [tex]\(632 - 691 = -59\)[/tex]
- Difference between the second and third terms: [tex]\(573 - 632 = -59\)[/tex]
- Difference between the third and fourth terms: [tex]\(514 - 573 = -59\)[/tex]
Since the differences are [tex]\(-59\)[/tex], [tex]\(-59\)[/tex], and [tex]\(-59\)[/tex] which are consistent, this sequence is arithmetic with a common difference of [tex]\(-59\)[/tex].
4. Sequence: [tex]\(\{845, 169, 33.8, 6.76, \ldots\}\)[/tex]
- Difference between the first and second terms: [tex]\(169 - 845 = -676\)[/tex]
- Difference between the second and third terms: [tex]\(33.8 - 169 = -135.2\)[/tex]
- Difference between the third and fourth terms: [tex]\(6.76 - 33.8 = -27.04\)[/tex]
Since the differences are [tex]\(-676\)[/tex], [tex]\(-135.2\)[/tex], and [tex]\(-27.04\)[/tex] which are not consistent, this sequence is not arithmetic.
Out of all the sequences provided, the second sequence [tex]\(\{232, 354, 476, 598, \ldots\}\)[/tex] is a consistent arithmetic sequence with a common difference of [tex]\(122\)[/tex].
Thus, the infinite arithmetic sequence among the given options is:
[tex]$\{232, 354, 476, 598, \ldots\}$[/tex]
An arithmetic sequence is one in which the difference between any two consecutive terms is constant. This difference is known as the common difference.
Let's analyze each sequence step-by-step:
1. Sequence: [tex]\(\{724, -362, 181, -90.5\}\)[/tex]
- Difference between the first and second terms: [tex]\(-362 - 724 = -1086\)[/tex]
- Difference between the second and third terms: [tex]\(181 - (-362) = 181 + 362 = 543\)[/tex]
- Difference between the third and fourth terms: [tex]\(-90.5 - 181 = -271.5\)[/tex]
Since the differences are [tex]\(-1086\)[/tex], [tex]\(543\)[/tex], and [tex]\(-271.5\)[/tex] which are not consistent, this sequence is not arithmetic.
2. Sequence: [tex]\(\{232, 354, 476, 598, \ldots\}\)[/tex]
- Difference between the first and second terms: [tex]\(354 - 232 = 122\)[/tex]
- Difference between the second and third terms: [tex]\(476 - 354 = 122\)[/tex]
- Difference between the third and fourth terms: [tex]\(598 - 476 = 122\)[/tex]
Since the differences are [tex]\(122\)[/tex], [tex]\(122\)[/tex], and [tex]\(122\)[/tex] which are consistent, this sequence is arithmetic with a common difference of [tex]\(122\)[/tex].
3. Sequence: [tex]\(\{691, 632, 573, 514\}\)[/tex]
- Difference between the first and second terms: [tex]\(632 - 691 = -59\)[/tex]
- Difference between the second and third terms: [tex]\(573 - 632 = -59\)[/tex]
- Difference between the third and fourth terms: [tex]\(514 - 573 = -59\)[/tex]
Since the differences are [tex]\(-59\)[/tex], [tex]\(-59\)[/tex], and [tex]\(-59\)[/tex] which are consistent, this sequence is arithmetic with a common difference of [tex]\(-59\)[/tex].
4. Sequence: [tex]\(\{845, 169, 33.8, 6.76, \ldots\}\)[/tex]
- Difference between the first and second terms: [tex]\(169 - 845 = -676\)[/tex]
- Difference between the second and third terms: [tex]\(33.8 - 169 = -135.2\)[/tex]
- Difference between the third and fourth terms: [tex]\(6.76 - 33.8 = -27.04\)[/tex]
Since the differences are [tex]\(-676\)[/tex], [tex]\(-135.2\)[/tex], and [tex]\(-27.04\)[/tex] which are not consistent, this sequence is not arithmetic.
Out of all the sequences provided, the second sequence [tex]\(\{232, 354, 476, 598, \ldots\}\)[/tex] is a consistent arithmetic sequence with a common difference of [tex]\(122\)[/tex].
Thus, the infinite arithmetic sequence among the given options is:
[tex]$\{232, 354, 476, 598, \ldots\}$[/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
