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Answer :
Sure! Let's analyze the problem step by step:
We're given a sequence: [tex]\(14, 24, 34, 44, 54, \ldots\)[/tex], which is an arithmetic sequence. This means that the difference between consecutive terms is constant.
Step 1: Find the common difference.
To find the common difference, subtract the first term from the second term:
[tex]\[
24 - 14 = 10
\][/tex]
So, the common difference is [tex]\(10\)[/tex].
Step 2: Identify the first term.
The first term of the sequence is clearly given as [tex]\(14\)[/tex].
Step 3: Write the recursive function.
A recursive function for an arithmetic sequence with a common difference [tex]\(d\)[/tex] and a first term [tex]\(f(1)\)[/tex] is generally expressed as:
[tex]\[
f(n+1) = f(n) + d
\][/tex]
Given that:
- The common difference [tex]\(d = 10\)[/tex]
- The first term [tex]\(f(1) = 14\)[/tex]
The recursive function is:
[tex]\[
f(n+1) = f(n) + 10 \quad \text{where} \quad f(1) = 14
\][/tex]
Conclusion:
The correct statement that describes 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]."
We're given a sequence: [tex]\(14, 24, 34, 44, 54, \ldots\)[/tex], which is an arithmetic sequence. This means that the difference between consecutive terms is constant.
Step 1: Find the common difference.
To find the common difference, subtract the first term from the second term:
[tex]\[
24 - 14 = 10
\][/tex]
So, the common difference is [tex]\(10\)[/tex].
Step 2: Identify the first term.
The first term of the sequence is clearly given as [tex]\(14\)[/tex].
Step 3: Write the recursive function.
A recursive function for an arithmetic sequence with a common difference [tex]\(d\)[/tex] and a first term [tex]\(f(1)\)[/tex] is generally expressed as:
[tex]\[
f(n+1) = f(n) + d
\][/tex]
Given that:
- The common difference [tex]\(d = 10\)[/tex]
- The first term [tex]\(f(1) = 14\)[/tex]
The recursive function is:
[tex]\[
f(n+1) = f(n) + 10 \quad \text{where} \quad f(1) = 14
\][/tex]
Conclusion:
The correct statement that describes 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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