At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To describe the given sequence [tex]\(-34, -21, -8, 5, \ldots\)[/tex] with a recursively defined function, we need to determine two main components:
1. The first term of the sequence.
2. The common difference between each term in the sequence.
Here are the steps to complete each part of the function:
1. Identify the first term:
- The first term of the sequence is the value at the first position.
- From the sequence provided ([tex]\(-34, -21, -8, 5, \ldots\)[/tex]), the first term is [tex]\( -34 \)[/tex].
2. Determine the common difference:
- The common difference in a sequence is found by subtracting the previous term from the next term.
- Subtract the first term from the second term in the sequence:
[tex]\[ -21 - (-34) = -21 + 34 = 13 \][/tex]
- The common difference is [tex]\( 13 \)[/tex].
3. Formulate the recursive function:
- The recursive formula is: [tex]\( f(n) = f(n-1) + \text{common difference} \)[/tex].
- In this case, [tex]\( f(n) = f(n-1) + 13 \)[/tex].
Using this information, we can complete the recursively defined function:
[tex]\[ \begin{array}{l} f(1) = -34 \\ f(n) = f(n-1) + 13 \\ \text{for } n = 2, 3, 4, \ldots \end{array} \][/tex]
Summarizing:
[tex]\[ \begin{array}{l} f(1) = -34 \\ f(n) = f(n-1) + 13 \\ \text{for } n = 2, 3, 4, \ldots \end{array} \][/tex]
So, the correct numbers to fill in the statements are:
[tex]\[ \begin{array}{l} f(1)= -34 \\ f(n)=f(n-1)+ 13 \\ \text{for } n=2,3,4, \ldots \\ \end{array} \][/tex]
1. The first term of the sequence.
2. The common difference between each term in the sequence.
Here are the steps to complete each part of the function:
1. Identify the first term:
- The first term of the sequence is the value at the first position.
- From the sequence provided ([tex]\(-34, -21, -8, 5, \ldots\)[/tex]), the first term is [tex]\( -34 \)[/tex].
2. Determine the common difference:
- The common difference in a sequence is found by subtracting the previous term from the next term.
- Subtract the first term from the second term in the sequence:
[tex]\[ -21 - (-34) = -21 + 34 = 13 \][/tex]
- The common difference is [tex]\( 13 \)[/tex].
3. Formulate the recursive function:
- The recursive formula is: [tex]\( f(n) = f(n-1) + \text{common difference} \)[/tex].
- In this case, [tex]\( f(n) = f(n-1) + 13 \)[/tex].
Using this information, we can complete the recursively defined function:
[tex]\[ \begin{array}{l} f(1) = -34 \\ f(n) = f(n-1) + 13 \\ \text{for } n = 2, 3, 4, \ldots \end{array} \][/tex]
Summarizing:
[tex]\[ \begin{array}{l} f(1) = -34 \\ f(n) = f(n-1) + 13 \\ \text{for } n = 2, 3, 4, \ldots \end{array} \][/tex]
So, the correct numbers to fill in the statements are:
[tex]\[ \begin{array}{l} f(1)= -34 \\ f(n)=f(n-1)+ 13 \\ \text{for } n=2,3,4, \ldots \\ \end{array} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.