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Answer :
To solve this question, we need to determine the correct statement about the recursive function used to generate the given arithmetic sequence: 14, 24, 34, 44, 54, ...
1. Identify the Common Difference: An arithmetic sequence is defined by a constant difference between consecutive terms. To find this common difference, we subtract the first term from the second term:
[tex]\[
24 - 14 = 10
\][/tex]
So, the common difference is 10.
2. Write the Recursive Function: In a recursive function for an arithmetic sequence, each term is generated by adding the common difference to the previous term. The recursive function can be written as:
[tex]\[
f(n+1) = f(n) + 10
\][/tex]
Here, [tex]\( f(n) \)[/tex] is the current term of the sequence, and [tex]\( f(n+1) \)[/tex] is the next term.
3. Determine the Initial Value: The initial value for the recursive function is the first term of the sequence, which is 14. Therefore, we set:
[tex]\[
f(1) = 14
\][/tex]
Putting it all together, the correct statement about the recursive function is: "The common difference is 10, so the function is [tex]\( f(n+1)=f(n)+10 \)[/tex] where [tex]\( f(1)=14 \)[/tex]."
1. Identify the Common Difference: An arithmetic sequence is defined by a constant difference between consecutive terms. To find this common difference, we subtract the first term from the second term:
[tex]\[
24 - 14 = 10
\][/tex]
So, the common difference is 10.
2. Write the Recursive Function: In a recursive function for an arithmetic sequence, each term is generated by adding the common difference to the previous term. The recursive function can be written as:
[tex]\[
f(n+1) = f(n) + 10
\][/tex]
Here, [tex]\( f(n) \)[/tex] is the current term of the sequence, and [tex]\( f(n+1) \)[/tex] is the next term.
3. Determine the Initial Value: The initial value for the recursive function is the first term of the sequence, which is 14. Therefore, we set:
[tex]\[
f(1) = 14
\][/tex]
Putting it all together, the correct statement about the recursive function is: "The common difference is 10, so the function is [tex]\( f(n+1)=f(n)+10 \)[/tex] where [tex]\( f(1)=14 \)[/tex]."
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