We appreciate your visit to Select the correct type of sequence and recursive function for the sequence below tex 34 40 46 52 tex A Arithmetic sequence tex f 1. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To identify the type of sequence and the corresponding recursive function for the sequence [tex]\(34, 40, 46, 52\)[/tex], you can follow these steps:
1. Identify the Type of Sequence:
- An arithmetic sequence is one in which each term is obtained by adding a constant value to the previous term.
- A geometric sequence is one in which each term is obtained by multiplying the previous term by a constant value.
2. Check if the Sequence is Arithmetic:
- Calculate the differences between consecutive terms:
- [tex]\(40 - 34 = 6\)[/tex]
- [tex]\(46 - 40 = 6\)[/tex]
- [tex]\(52 - 46 = 6\)[/tex]
- Since the differences are the same, [tex]\(6\)[/tex] in each case, the sequence is an arithmetic sequence.
3. Determine the Recursive Function for the Arithmetic Sequence:
- The first term of the sequence is [tex]\(f(1) = 34\)[/tex].
- The recursive formula for an arithmetic sequence is: [tex]\(f(n) = f(n-1) + d\)[/tex], where [tex]\(d\)[/tex] is the common difference. In this case, the common difference [tex]\(d = 6\)[/tex].
Putting it all together, the sequence is an arithmetic sequence with the recursive function:
- Arithmetic sequence
- Recursive function: [tex]\(f(1) = 34 ; f(n) = f(n-1) + 6\)[/tex], for [tex]\(n \geq 2\)[/tex]
Therefore, the correct answer is:
Arithmetic sequence; [tex]\(f(1) = 34 ; f(n) = f(n-1) + 6\)[/tex], for [tex]\(n \geq 2\)[/tex]
1. Identify the Type of Sequence:
- An arithmetic sequence is one in which each term is obtained by adding a constant value to the previous term.
- A geometric sequence is one in which each term is obtained by multiplying the previous term by a constant value.
2. Check if the Sequence is Arithmetic:
- Calculate the differences between consecutive terms:
- [tex]\(40 - 34 = 6\)[/tex]
- [tex]\(46 - 40 = 6\)[/tex]
- [tex]\(52 - 46 = 6\)[/tex]
- Since the differences are the same, [tex]\(6\)[/tex] in each case, the sequence is an arithmetic sequence.
3. Determine the Recursive Function for the Arithmetic Sequence:
- The first term of the sequence is [tex]\(f(1) = 34\)[/tex].
- The recursive formula for an arithmetic sequence is: [tex]\(f(n) = f(n-1) + d\)[/tex], where [tex]\(d\)[/tex] is the common difference. In this case, the common difference [tex]\(d = 6\)[/tex].
Putting it all together, the sequence is an arithmetic sequence with the recursive function:
- Arithmetic sequence
- Recursive function: [tex]\(f(1) = 34 ; f(n) = f(n-1) + 6\)[/tex], for [tex]\(n \geq 2\)[/tex]
Therefore, the correct answer is:
Arithmetic sequence; [tex]\(f(1) = 34 ; f(n) = f(n-1) + 6\)[/tex], for [tex]\(n \geq 2\)[/tex]
Thanks for taking the time to read Select the correct type of sequence and recursive function for the sequence below tex 34 40 46 52 tex A Arithmetic sequence tex f 1. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
