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Answer :
To solve the problem of identifying the recursive function for the given arithmetic sequence, we need to follow these steps:
1. Identify the Sequence:
The sequence given is [tex]\( 14, 24, 34, 44, 54, \ldots \)[/tex].
2. Determine the Common Difference:
An arithmetic sequence has a constant difference between consecutive terms. To find this difference, subtract the first term from the second term:
[tex]\[
24 - 14 = 10
\][/tex]
Therefore, the common difference is [tex]\( 10 \)[/tex].
3. Identify the First Term:
The first term of the sequence is clearly [tex]\( 14 \)[/tex].
4. Write the Recursive Function:
Using the identified common difference and the first term, the recursive formula for the sequence can be expressed as:
[tex]\[
f(n+1) = f(n) + 10 \quad \text{where} \quad f(1) = 14
\][/tex]
Given these calculations, the correct statement describing the recursive function used to generate the 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]."
1. Identify the Sequence:
The sequence given is [tex]\( 14, 24, 34, 44, 54, \ldots \)[/tex].
2. Determine the Common Difference:
An arithmetic sequence has a constant difference between consecutive terms. To find this difference, subtract the first term from the second term:
[tex]\[
24 - 14 = 10
\][/tex]
Therefore, the common difference is [tex]\( 10 \)[/tex].
3. Identify the First Term:
The first term of the sequence is clearly [tex]\( 14 \)[/tex].
4. Write the Recursive Function:
Using the identified common difference and the first term, the recursive formula for the sequence can be expressed as:
[tex]\[
f(n+1) = f(n) + 10 \quad \text{where} \quad f(1) = 14
\][/tex]
Given these calculations, the correct statement describing the recursive function used to generate the 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]."
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