Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Which of the following are arithmetic sequences? Check all that apply.

A. [tex]2, 6, 18, 54, \ldots[/tex]

B. [tex]2, 2, 2, 2, 2, \ldots[/tex]

C. [tex]100, 230, 360, 490, \ldots[/tex]

D. [tex]1, 2, 3, 4, 5, 6, \ldots[/tex]

Sagot :

GinnyAnswer
To determine which of the given sequences are arithmetic, let's review the definition of an arithmetic sequence:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference.

Let's analyze each sequence step by step:

### Sequence A: [tex]\(2, 6, 18, 54, \ldots\)[/tex]

1. Calculate the differences between consecutive terms:
- [tex]\(6 - 2 = 4\)[/tex]
- [tex]\(18 - 6 = 12\)[/tex]
- [tex]\(54 - 18 = 36\)[/tex]

2. The differences are [tex]\(4, 12, 36\)[/tex] and they are not constant.

Since the differences are not consistent, sequence [tex]\(A\)[/tex] is not an arithmetic sequence.

### Sequence B: [tex]\(2, 2, 2, 2, 2, \ldots\)[/tex]

1. Calculate the differences between consecutive terms:
- [tex]\(2 - 2 = 0\)[/tex]
- [tex]\(2 - 2 = 0\)[/tex]
- [tex]\(2 - 2 = 0\)[/tex]
- [tex]\(2 - 2 = 0\)[/tex]

2. All differences are [tex]\(0\)[/tex], which is consistent.

Since the difference between all consecutive terms is constant, sequence [tex]\(B\)[/tex] is an arithmetic sequence.

### Sequence C: [tex]\(100, 230, 360, 490, \ldots\)[/tex]

1. Calculate the differences between consecutive terms:
- [tex]\(230 - 100 = 130\)[/tex]
- [tex]\(360 - 230 = 130\)[/tex]
- [tex]\(490 - 360 = 130\)[/tex]

2. The differences are [tex]\(130, 130, 130\)[/tex] and they are constant.

Since the difference between all consecutive terms is constant, sequence [tex]\(C\)[/tex] is an arithmetic sequence.

### Sequence D: [tex]\(1, 2, 3, 4, 5, 6, \ldots\)[/tex]

1. Calculate the differences between consecutive terms:
- [tex]\(2 - 1 = 1\)[/tex]
- [tex]\(3 - 2 = 1\)[/tex]
- [tex]\(4 - 3 = 1\)[/tex]
- [tex]\(5 - 4 = 1\)[/tex]
- [tex]\(6 - 5 = 1\)[/tex]

2. The differences are [tex]\(1, 1, 1, 1, 1\)[/tex] and they are constant.

Since the difference between all consecutive terms is constant, sequence [tex]\(D\)[/tex] is an arithmetic sequence.

### Conclusion

After analyzing each sequence, we can conclude that the following sequences are arithmetic:

- Sequence B: [tex]\(2, 2, 2, 2, 2, \ldots\)[/tex]
- Sequence C: [tex]\(100, 230, 360, 490, \ldots\)[/tex]
- Sequence D: [tex]\(1, 2, 3, 4, 5, 6, \ldots\)[/tex]

Sequence [tex]\(A\)[/tex] is not an arithmetic sequence. Therefore, the arithmetic sequences are:

- Sequence B
- Sequence C
- Sequence D
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.