2. Which recursively defined function has a first term equal to 10 and a common difference of 4? 1. f(1) 10 f(2) = f(2-1) +4 2. f(1) 4 f(2) – f(z - 1) + 10 f(1) 10 3. f(2) = 4f(2- 1) 4. S(1) 4 f(2) 10f(z- 1)
2. Which recursively defined function has a first term equal to 10 and a common difference of 4? 1. f(1) 10 f(2) = f(2-1) +4 2. f(1) 4 f(2) – f(z - 1) + 10 f(1) 10 3. f(2) = 4f(2- 1) 4. S(1) 4 f(2) 10f(z- 1)
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
Topic Video
Question
![### Question
Which recursively defined function has a first term equal to 10 and a common difference of 4?
### Options
1.
\[f(1) = 10\]
\[f(x) = f(x-1) + 4\]
2.
\[f(1) = 4\]
\[f(x) = f(x-1) + 10\]
3.
\[f(1) = 10\]
\[f(x) = 4f(x-1)\]
4.
\[f(1) = 4\]
\[f(x) = 10f(x-1)\]
### Explanation
To determine which of these recursively defined functions has a first term equal to 10 and a common difference of 4, consider the recursive formulas and their initial conditions:
- **Option 1:**
- Initial Condition: \(f(1) = 10\)
- Recursive Formula: \(f(x) = f(x-1) + 4\)
- This implies the sequence starts at 10 and increases by 4 each step, thus having a common difference of 4.
- **Option 2:**
- Initial Condition: \(f(1) = 4\)
- Recursive Formula: \(f(x) = f(x-1) + 10\)
- This sequence starts at 4 and increases by 10, which does not match the required first term or common difference.
- **Option 3:**
- Initial Condition: \(f(1) = 10\)
- Recursive Formula: \(f(x) = 4f(x-1)\)
- This generates a geometric sequence, not an arithmetic one with a common difference of 4.
- **Option 4:**
- Initial Condition: \(f(1) = 4\)
- Recursive Formula: \(f(x) = 10f(x-1)\)
- This also generates a geometric sequence, not matching the conditions.
### Correct Answer
**Option 1:**
\[f(1) = 10\]
\[f(x) = f(x-1) + 4\]
This option meets the conditions with the first term being 10 and a common difference of 4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39d59398-4789-4d27-a5be-d0cd6324ea81%2F5999607d-9dbb-4735-8005-4b0ad0787ca6%2Ft8x0xcc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question
Which recursively defined function has a first term equal to 10 and a common difference of 4?
### Options
1.
\[f(1) = 10\]
\[f(x) = f(x-1) + 4\]
2.
\[f(1) = 4\]
\[f(x) = f(x-1) + 10\]
3.
\[f(1) = 10\]
\[f(x) = 4f(x-1)\]
4.
\[f(1) = 4\]
\[f(x) = 10f(x-1)\]
### Explanation
To determine which of these recursively defined functions has a first term equal to 10 and a common difference of 4, consider the recursive formulas and their initial conditions:
- **Option 1:**
- Initial Condition: \(f(1) = 10\)
- Recursive Formula: \(f(x) = f(x-1) + 4\)
- This implies the sequence starts at 10 and increases by 4 each step, thus having a common difference of 4.
- **Option 2:**
- Initial Condition: \(f(1) = 4\)
- Recursive Formula: \(f(x) = f(x-1) + 10\)
- This sequence starts at 4 and increases by 10, which does not match the required first term or common difference.
- **Option 3:**
- Initial Condition: \(f(1) = 10\)
- Recursive Formula: \(f(x) = 4f(x-1)\)
- This generates a geometric sequence, not an arithmetic one with a common difference of 4.
- **Option 4:**
- Initial Condition: \(f(1) = 4\)
- Recursive Formula: \(f(x) = 10f(x-1)\)
- This also generates a geometric sequence, not matching the conditions.
### Correct Answer
**Option 1:**
\[f(1) = 10\]
\[f(x) = f(x-1) + 4\]
This option meets the conditions with the first term being 10 and a common difference of 4.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
