in the standard fo ... Write the arithmetic sequence - 4, - 10, - 16, – 22, An %3D DVideo M Message instructor D Post to forum Question Write the arithmetic sequence 24, 16, 8, 0, ... in the standard form:
in the standard fo ... Write the arithmetic sequence - 4, - 10, - 16, – 22, An %3D DVideo M Message instructor D Post to forum Question Write the arithmetic sequence 24, 16, 8, 0, ... in the standard form:
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![The image contains educational content related to arithmetic sequences. However, certain portions of the image are obscured with blue lines, blocking some specific details and instructions. Here is a transcription of the visible parts of the image:
---
### Arithmetic Sequences
1. Write the arithmetic sequence 24, 16, 8, 0, ... in the standard form:
\[
a_n = \_\_\_
\]
2. Write the arithmetic sequence -4, -10, -16, -22, ... in the standard form:
\[
a_n = \_\_\_
\]
---
Additional Details:
- There are underlined blank spaces following "a_n =" in each exercise, indicating that the students are expected to fill in the appropriate formula for the nth term of the given arithmetic sequences.
- Elements of the user interface, such as options for video help, messaging the instructor, and submission buttons, suggest that this educational content might be part of an online learning platform.
### Explanation for Given Arithmetic Sequences
An arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant. This constant is called the common difference (d).
- **Sequence 1: 24, 16, 8, 0, ...**
- First term (a_1) = 24
- Common difference (d) = 16 - 24 = -8
The standard form of the nth term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1)d
\]
For the first sequence, we get:
\[
a_n = 24 + (n - 1)(-8)
\]
- **Sequence 2: -4, -10, -16, -22, ...**
- First term (a_1) = -4
- Common difference (d) = -10 - (-4) = -6
Using the standard form:
\[
a_n = -4 + (n - 1)(-6)
\]
Students would be expected to complete these sequences by writing them in the standard form based on the formula provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7921e840-b4be-4997-af5c-a45fa0acee7f%2Ffc6133f3-dce3-4df1-85c5-5fc3f6c20207%2Fxxb53k8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains educational content related to arithmetic sequences. However, certain portions of the image are obscured with blue lines, blocking some specific details and instructions. Here is a transcription of the visible parts of the image:
---
### Arithmetic Sequences
1. Write the arithmetic sequence 24, 16, 8, 0, ... in the standard form:
\[
a_n = \_\_\_
\]
2. Write the arithmetic sequence -4, -10, -16, -22, ... in the standard form:
\[
a_n = \_\_\_
\]
---
Additional Details:
- There are underlined blank spaces following "a_n =" in each exercise, indicating that the students are expected to fill in the appropriate formula for the nth term of the given arithmetic sequences.
- Elements of the user interface, such as options for video help, messaging the instructor, and submission buttons, suggest that this educational content might be part of an online learning platform.
### Explanation for Given Arithmetic Sequences
An arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant. This constant is called the common difference (d).
- **Sequence 1: 24, 16, 8, 0, ...**
- First term (a_1) = 24
- Common difference (d) = 16 - 24 = -8
The standard form of the nth term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1)d
\]
For the first sequence, we get:
\[
a_n = 24 + (n - 1)(-8)
\]
- **Sequence 2: -4, -10, -16, -22, ...**
- First term (a_1) = -4
- Common difference (d) = -10 - (-4) = -6
Using the standard form:
\[
a_n = -4 + (n - 1)(-6)
\]
Students would be expected to complete these sequences by writing them in the standard form based on the formula provided.
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