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,...
Related questions
Question
![**Arithmetic Sequence Problem**
**Question:**
Which term of the arithmetic sequence \(1, 9, 17, 25, \ldots\) is 345?
**Answer:**
It is the \(\_\_\_\) th term.
**Explanation:**
This problem asks you to determine the position \(n\) of the term 345 in the given arithmetic sequence. An arithmetic sequence has a constant difference between consecutive terms. You can use the formula for the \(n\)th term of an arithmetic sequence to find the solution:
\[ a_n = a_1 + (n-1) \cdot d, \]
where:
- \( a_n \) is the \(n\)th term,
- \( a_1 \) is the first term of the sequence,
- \( d \) is the common difference,
- \( n \) is the term number.
**Steps to Solve:**
1. Identify the first term (\(a_1\)) and the common difference (\(d\)) from the sequence.
2. Set \(a_n = 345\), substitute the known values, and solve for \(n\).
This calculation allows you to fill in the blank with the correct term number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd9b0b5a-0679-4fc8-95b3-d7301c596838%2F22eadb07-02ab-442a-922e-f87fe2978bb6%2F0ucyq4k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Arithmetic Sequence Problem**
**Question:**
Which term of the arithmetic sequence \(1, 9, 17, 25, \ldots\) is 345?
**Answer:**
It is the \(\_\_\_\) th term.
**Explanation:**
This problem asks you to determine the position \(n\) of the term 345 in the given arithmetic sequence. An arithmetic sequence has a constant difference between consecutive terms. You can use the formula for the \(n\)th term of an arithmetic sequence to find the solution:
\[ a_n = a_1 + (n-1) \cdot d, \]
where:
- \( a_n \) is the \(n\)th term,
- \( a_1 \) is the first term of the sequence,
- \( d \) is the common difference,
- \( n \) is the term number.
**Steps to Solve:**
1. Identify the first term (\(a_1\)) and the common difference (\(d\)) from the sequence.
2. Set \(a_n = 345\), substitute the known values, and solve for \(n\).
This calculation allows you to fill in the blank with the correct term number.
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