Given an Arithmetic Series that contains the following terms: t(4) = 5, t(7) = 20, and the total number of terms is 20. Use the options below and answer each question. What is t (11)? How can you represent the series in Sigma Form? What is S (n)? 20 20 20 20 Σ Σ 4n – 15 4n – 10 > 5n – 15 5n – 10 R: n=1 C: n=1 D: n=1 n=1 A: Sigma Form: choose your answer. S(n)= type your answer. t(11)= type your answer...
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![### Given an Arithmetic Series
The problem presents an arithmetic series with the following terms:
- \( t(4) = 5 \)
- \( t(7) = 20 \)
The total number of terms in the series is 20. Answer each of the following questions based on this information.
**Questions to be Answered:**
1. **What is \( t(11) \)?**
2. **How can you represent the series in Sigma Form?**
3. **What is \( S(n) \)?**
Below the question prompts, there are four options (A, B, C, D) which display different series in Sigma notation:
**Option A:**
\[ \sum_{n=1}^{20} (4n - 15) \]
**Option B:**
\[ \sum_{n=1}^{20} (4n - 10) \]
**Option C:**
\[ \sum_{n=1}^{20} (5n - 15) \]
**Option D:**
\[ \sum_{n=1}^{20} (5n - 10) \]
Additionally, below these options, there are fields to be filled in by the user:
- **\( t(11) \) Field:** "type your answer..."
- **Sigma Form Dropdown:** "choose your answer..."
- **\( S(n) \) Field:** "type your answer..."
### Explanation Notes:
- **Sigma Notation:** This is a way to represent a sum of terms in a series.
- **Arithmetic Series:** A sequence of numbers in which the difference of any two successive members is a constant.
- **\( t(n) \):** Represents the nth term of the series.
- **\( S(n) \):** Represents the sum of the first n terms of the series.
To find the options correctly and determine the function for the arithmetic series, organize the information given and use standard formulas for arithmetic sequences and series.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a6b5d45-cf69-4315-8afb-f578b0e1f7f7%2Fe0846413-cac2-4c61-b5c3-65c6c3ab22fa%2Faukydkj_processed.jpeg&w=3840&q=75)
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