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**Title: Finding the General Term of an Arithmetic Sequence** **Objective:** Learn how to write a formula for the general term of an arithmetic sequence and use it to find specific terms. **Problem Statement:** Write a formula for the general term of each arithmetic sequence. Then use the formula to find the tenth term (a₁₀). **Given Sequence:** - First term (a₁): 6 - Second term: 1 - Third term: -4 - Fourth term: -9 **Solution Steps:** 1. **Determine the first term (a₁):** - The first term of the sequence is 6. 2. **Find the common difference (d):** - Subtract the first term from the second term: \(1 - 6 = -5\). - The common difference (d) is -5. 3. **General formula for the nth term of an arithmetic sequence:** \[ a_n = a_1 + (n - 1) \cdot d \] Substituting the known values, we get: \[ a_n = 6 + (n - 1)(-5) \] 4. **Find the tenth term (a₁₀):** \[ a_{10} = 6 + (10 - 1)(-5) \] \[ a_{10} = 6 + 9(-5) \] \[ a_{10} = 6 - 45 \] \[ a_{10} = -39 \] **Conclusion:** The general term of the sequence is \(a_n = 6 + (n - 1)(-5)\), and the tenth term \(a₁₀\) is -39.

**Title: Finding the General Term of an Arithmetic Sequence** **Objective:** Learn how to write a formula for the general term of an arithmetic sequence and use it to find specific terms. **Problem Statement:** Write a formula for the general term of each arithmetic sequence. Then use the formula to find the tenth term (a₁₀). **Given Sequence:** - First term (a₁): 6 - Second term: 1 - Third term: -4 - Fourth term: -9 **Solution Steps:** 1. **Determine the first term (a₁):** - The first term of the sequence is 6. 2. **Find the common difference (d):** - Subtract the first term from the second term: \(1 - 6 = -5\). - The common difference (d) is -5. 3. **General formula for the nth term of an arithmetic sequence:** \[ a_n = a_1 + (n - 1) \cdot d \] Substituting the known values, we get: \[ a_n = 6 + (n - 1)(-5) \] 4. **Find the tenth term (a₁₀):** \[ a_{10} = 6 + (10 - 1)(-5) \] \[ a_{10} = 6 + 9(-5) \] \[ a_{10} = 6 - 45 \] \[ a_{10} = -39 \] **Conclusion:** The general term of the sequence is \(a_n = 6 + (n - 1)(-5)\), and the tenth term \(a₁₀\) is -39.

Algebra and Trigonometry (6th Edition)
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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**Title: Finding the General Term of an Arithmetic Sequence** **Objective:** Learn how to write a formula for the general term of an arithmetic sequence and use it to find specific terms. **Problem Statement:** Write a formula for the general term of each arithmetic sequence. Then use the formula to find the tenth term (a₁₀). **Given Sequence:** - First term (a₁): 6 - Second term: 1 - Third term: -4 - Fourth term: -9 **Solution Steps:** 1. **Determine the first term (a₁):** - The first term of the sequence is 6. 2. **Find the common difference (d):** - Subtract the first term from the second term: \(1 - 6 = -5\). - The common difference (d) is -5. 3. **General formula for the nth term of an arithmetic sequence:** \[ a_n = a_1 + (n - 1) \cdot d \] Substituting the known values, we get: \[ a_n = 6 + (n - 1)(-5) \] 4. **Find the tenth term (a₁₀):** \[ a_{10} = 6 + (10 - 1)(-5) \] \[ a_{10} = 6 + 9(-5) \] \[ a_{10} = 6 - 45 \] \[ a_{10} = -39 \] **Conclusion:** The general term of the sequence is \(a_n = 6 + (n - 1)(-5)\), and the tenth term \(a₁₀\) is -39.
Transcribed Image Text:**Title: Finding the General Term of an Arithmetic Sequence** **Objective:** Learn how to write a formula for the general term of an arithmetic sequence and use it to find specific terms. **Problem Statement:** Write a formula for the general term of each arithmetic sequence. Then use the formula to find the tenth term (a₁₀). **Given Sequence:** - First term (a₁): 6 - Second term: 1 - Third term: -4 - Fourth term: -9 **Solution Steps:** 1. **Determine the first term (a₁):** - The first term of the sequence is 6. 2. **Find the common difference (d):** - Subtract the first term from the second term: \(1 - 6 = -5\). - The common difference (d) is -5. 3. **General formula for the nth term of an arithmetic sequence:** \[ a_n = a_1 + (n - 1) \cdot d \] Substituting the known values, we get: \[ a_n = 6 + (n - 1)(-5) \] 4. **Find the tenth term (a₁₀):** \[ a_{10} = 6 + (10 - 1)(-5) \] \[ a_{10} = 6 + 9(-5) \] \[ a_{10} = 6 - 45 \] \[ a_{10} = -39 \] **Conclusion:** The general term of the sequence is \(a_n = 6 + (n - 1)(-5)\), and the tenth term \(a₁₀\) is -39.
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