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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![### Arithmetic Series Problems
In this exercise, you are tasked with finding the sum \( S_n \) for each given arithmetic series.
**Problem 7:**
Given:
- First term, \( a_1 = 12 \)
- Last term, \( a_n = 117 \)
- Number of terms, \( n = 36 \)
**Problem 8:**
Series: \( 4 + 10 + 16 + \cdots + 106 \)
**Problem 9:**
Summation notation:
\[ \sum_{n=2}^{29} (3n + 1) \]
To solve these problems, you will usually employ the formula for the sum of an arithmetic series:
\[ S_n = \frac{n}{2} (a_1 + a_n) \]
Or, for a general arithmetic series where you may need to find the number of terms or other specific details, you might also use the formula:
\[ a_n = a_1 + (n-1)d \]
where \( d \) is the common difference between the terms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafda5510-80e5-4cd6-ab69-bbe084c7367a%2Fefdb2835-5dc9-471b-bacb-b9aab2be229f%2F1mth7l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Arithmetic Series Problems
In this exercise, you are tasked with finding the sum \( S_n \) for each given arithmetic series.
**Problem 7:**
Given:
- First term, \( a_1 = 12 \)
- Last term, \( a_n = 117 \)
- Number of terms, \( n = 36 \)
**Problem 8:**
Series: \( 4 + 10 + 16 + \cdots + 106 \)
**Problem 9:**
Summation notation:
\[ \sum_{n=2}^{29} (3n + 1) \]
To solve these problems, you will usually employ the formula for the sum of an arithmetic series:
\[ S_n = \frac{n}{2} (a_1 + a_n) \]
Or, for a general arithmetic series where you may need to find the number of terms or other specific details, you might also use the formula:
\[ a_n = a_1 + (n-1)d \]
where \( d \) is the common difference between the terms.
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