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Answer :
To determine the correct recursive function used to generate the sequence [tex]\(4, 24, 34, 44, 54, \ldots\)[/tex], we need to find the pattern in the differences between consecutive numbers:
1. Calculate the difference between the first few terms:
- [tex]\(24 - 4 = 20\)[/tex]
- [tex]\(34 - 24 = 10\)[/tex]
- [tex]\(44 - 34 = 10\)[/tex]
- [tex]\(54 - 44 = 10\)[/tex]
2. Observe that after the first term, the common difference between consecutive numbers is consistently [tex]\(10\)[/tex].
3. This indicates the sequence follows an arithmetic pattern with a common difference of [tex]\(10\)[/tex], and the starting term [tex]\(f(1) = 4\)[/tex].
Therefore, the recursive function that describes this arithmetic sequence is [tex]\(f(n+1) = f(n) + 10\)[/tex] where [tex]\(f(1) = 4\)[/tex].
This explanation matches the sequence generated. The common difference is [tex]\(10\)[/tex], and the statement that accurately describes the sequence is:
"The common difference is 10, so the function is [tex]\(f(n+1)=f(n)+10\)[/tex] where [tex]\(f(1)=4\)[/tex]."
1. Calculate the difference between the first few terms:
- [tex]\(24 - 4 = 20\)[/tex]
- [tex]\(34 - 24 = 10\)[/tex]
- [tex]\(44 - 34 = 10\)[/tex]
- [tex]\(54 - 44 = 10\)[/tex]
2. Observe that after the first term, the common difference between consecutive numbers is consistently [tex]\(10\)[/tex].
3. This indicates the sequence follows an arithmetic pattern with a common difference of [tex]\(10\)[/tex], and the starting term [tex]\(f(1) = 4\)[/tex].
Therefore, the recursive function that describes this arithmetic sequence is [tex]\(f(n+1) = f(n) + 10\)[/tex] where [tex]\(f(1) = 4\)[/tex].
This explanation matches the sequence generated. The common difference is [tex]\(10\)[/tex], and the statement that accurately describes the sequence is:
"The common difference is 10, so the function is [tex]\(f(n+1)=f(n)+10\)[/tex] where [tex]\(f(1)=4\)[/tex]."
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