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Answer :
To solve the problem of finding the recursive function that generates the given arithmetic sequence, let's break down the steps:
1. Identify the Arithmetic Sequence: The sequence provided is 14, 24, 34, 44, 54, ...
2. Determine the Common Difference:
- To find the common difference in an arithmetic sequence, subtract any term from the next term.
- For example, 24 - 14 = 10, 34 - 24 = 10, and so on.
- Thus, the common difference is 10.
3. Identify the First Term:
- The first term of the sequence is clearly given as 14.
4. Write the Recursive Function:
- In a recursive function for an arithmetic sequence, the next term is found by adding the common difference to the current term.
- Therefore, the recursive function can be expressed as:
[tex]\[
f(n+1) = f(n) + 10
\][/tex]
where [tex]\( f(1) = 14 \)[/tex].
5. Conclusion:
- The correct statement that describes the recursive function for this sequence is:
"The common difference is 10, so the function is [tex]\( f(n+1) = f(n) + 10 \)[/tex] where [tex]\( f(1) = 14 \)[/tex]."
This means that starting from 14, you continue to add 10 to each term to get the next term, which perfectly matches the sequence given.
1. Identify the Arithmetic Sequence: The sequence provided is 14, 24, 34, 44, 54, ...
2. Determine the Common Difference:
- To find the common difference in an arithmetic sequence, subtract any term from the next term.
- For example, 24 - 14 = 10, 34 - 24 = 10, and so on.
- Thus, the common difference is 10.
3. Identify the First Term:
- The first term of the sequence is clearly given as 14.
4. Write the Recursive Function:
- In a recursive function for an arithmetic sequence, the next term is found by adding the common difference to the current term.
- Therefore, the recursive function can be expressed as:
[tex]\[
f(n+1) = f(n) + 10
\][/tex]
where [tex]\( f(1) = 14 \)[/tex].
5. Conclusion:
- The correct statement that describes the recursive function for this sequence is:
"The common difference is 10, so the function is [tex]\( f(n+1) = f(n) + 10 \)[/tex] where [tex]\( f(1) = 14 \)[/tex]."
This means that starting from 14, you continue to add 10 to each term to get the next term, which perfectly matches the sequence given.
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