Question
The following arithmetic sequence is given.
14, 11, 8, 5, ...
What are the next three terms?
A.4, 3, 2
B.2, −1, −4
C.3, 1, −2
D.1, −1, −3
14, 11, 8, 5, ...
What are the next three terms?
A.4, 3, 2
B.2, −1, −4
C.3, 1, −2
D.1, −1, −3
Answers
Answer
an = 3n + 17
B.an = −3n + 17
C.an = 3n − 17
D.an = 17n − 3
B.an = −3n + 17
C.an = 3n − 17
D.an = 17n − 3
Answered by
GPT-4o mini
To find the next three terms in the arithmetic sequence 14, 11, 8, 5, we first need to identify the common difference.
The common difference is calculated as follows:
11 - 14 = -3
8 - 11 = -3
5 - 8 = -3
So, the common difference is -3.
Now, to find the next three terms, we will continue subtracting 3 from the last term:
1. 5 - 3 = 2
2. 2 - 3 = -1
3. -1 - 3 = -4
Thus, the next three terms of the sequence are 2, -1, and -4.
Therefore, the answer is **B. 2, −1, −4.**
The common difference is calculated as follows:
11 - 14 = -3
8 - 11 = -3
5 - 8 = -3
So, the common difference is -3.
Now, to find the next three terms, we will continue subtracting 3 from the last term:
1. 5 - 3 = 2
2. 2 - 3 = -1
3. -1 - 3 = -4
Thus, the next three terms of the sequence are 2, -1, and -4.
Therefore, the answer is **B. 2, −1, −4.**
Answered by
GPT-4o mini
It seems like you've provided several expressions for a general term of a sequence, denoted as \( a_n \). However, you've not given the context for what you're asking.
Let’s analyze each option:
1. **A. \( a_n = 3n + 17 \)**
This represents a linear expression where the term increases by 3 for each subsequent value of \( n \).
2. **B. \( a_n = -3n + 17 \)**
This also represents a linear expression but decreases by 3 for each subsequent value of \( n\).
3. **C. \( a_n = 3n - 17 \)**
This is another linear expression that increases by 3 for each value of \( n \) but starts from -17 instead of 17.
4. **D. \( a_n = 17n - 3 \)**
This expression increases by 17 for each value of \( n\), starting from -3.
If you could clarify the question or provide a specific context for these expressions (like a problem statement or further instructions), I’d be happy to help you!
Let’s analyze each option:
1. **A. \( a_n = 3n + 17 \)**
This represents a linear expression where the term increases by 3 for each subsequent value of \( n \).
2. **B. \( a_n = -3n + 17 \)**
This also represents a linear expression but decreases by 3 for each subsequent value of \( n\).
3. **C. \( a_n = 3n - 17 \)**
This is another linear expression that increases by 3 for each value of \( n \) but starts from -17 instead of 17.
4. **D. \( a_n = 17n - 3 \)**
This expression increases by 17 for each value of \( n\), starting from -3.
If you could clarify the question or provide a specific context for these expressions (like a problem statement or further instructions), I’d be happy to help you!
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