Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Question:
What is the sum of the first 14 terms of the series \(9 + 2 - 5 - 12 - 19 - ...\)?
### Answer Choices:
- \( \text{A) } -25 \)
- \( \text{B) } -98 \)
- \( \text{C) } -511 \)
- \( \text{D) } -518 \)
### Explanation:
This question is about finding the sum of the first 14 terms of the given arithmetic series.
In an arithmetic series, the common difference \( d \) can be found by subtracting any term from the term that follows it. Let's find the common difference:
\( 2 - 9 = -7 \)
So, the common difference \( d = -7 \).
The first term \( a = 9 \).
The sum \( S_n \) of the first \( n \) terms of an arithmetic series can be calculated using the formula:
\[ S_n = \frac{n}{2} (2a + (n-1)d) \]
For \( n = 14 \):
\[ S_{14} = \frac{14}{2} \left(2 \times 9 + (14 - 1) \times -7 \right) \]
\[ S_{14} = 7 \left(18 + 13 \times -7 \right) \]
\[ S_{14} = 7 \left(18 - 91 \right) \]
\[ S_{14} = 7 \times -73 \]
\[ S_{14} = -511 \]
Therefore, the correct answer is \( -511 \), which corresponds to option C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3047b756-b2f4-4f66-ba10-7c0773ac07fd%2F9c1b045b-7a24-4c3c-be59-e0dd45ab7fb5%2Fgm9zswxa_processed.png&w=3840&q=75)
Transcribed Image Text:### Question:
What is the sum of the first 14 terms of the series \(9 + 2 - 5 - 12 - 19 - ...\)?
### Answer Choices:
- \( \text{A) } -25 \)
- \( \text{B) } -98 \)
- \( \text{C) } -511 \)
- \( \text{D) } -518 \)
### Explanation:
This question is about finding the sum of the first 14 terms of the given arithmetic series.
In an arithmetic series, the common difference \( d \) can be found by subtracting any term from the term that follows it. Let's find the common difference:
\( 2 - 9 = -7 \)
So, the common difference \( d = -7 \).
The first term \( a = 9 \).
The sum \( S_n \) of the first \( n \) terms of an arithmetic series can be calculated using the formula:
\[ S_n = \frac{n}{2} (2a + (n-1)d) \]
For \( n = 14 \):
\[ S_{14} = \frac{14}{2} \left(2 \times 9 + (14 - 1) \times -7 \right) \]
\[ S_{14} = 7 \left(18 + 13 \times -7 \right) \]
\[ S_{14} = 7 \left(18 - 91 \right) \]
\[ S_{14} = 7 \times -73 \]
\[ S_{14} = -511 \]
Therefore, the correct answer is \( -511 \), which corresponds to option C.
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