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Answer :
To solve the problem, we start by identifying the first term and the common difference of the arithmetic sequence.
1. The sequence is given by
[tex]$$14,\, 24,\, 34,\, 44,\, 54,\, \dots$$[/tex]
The first term is:
[tex]$$f(1) = 14.$$[/tex]
2. The common difference ([tex]$d$[/tex]) is found by subtracting the first term from the second term:
[tex]$$d = 24 - 14 = 10.$$[/tex]
3. In an arithmetic sequence, the recursive function has the form:
[tex]$$f(n+1) = f(n) + d.$$[/tex]
Substituting the values we found,
[tex]$$f(n+1) = f(n) + 10,$$[/tex]
with the initial condition:
[tex]$$f(1) = 14.$$[/tex]
4. Among the provided options, the statement that correctly describes 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]."
Thus, the correct answer is option 3.
1. The sequence is given by
[tex]$$14,\, 24,\, 34,\, 44,\, 54,\, \dots$$[/tex]
The first term is:
[tex]$$f(1) = 14.$$[/tex]
2. The common difference ([tex]$d$[/tex]) is found by subtracting the first term from the second term:
[tex]$$d = 24 - 14 = 10.$$[/tex]
3. In an arithmetic sequence, the recursive function has the form:
[tex]$$f(n+1) = f(n) + d.$$[/tex]
Substituting the values we found,
[tex]$$f(n+1) = f(n) + 10,$$[/tex]
with the initial condition:
[tex]$$f(1) = 14.$$[/tex]
4. Among the provided options, the statement that correctly describes 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]."
Thus, the correct answer is option 3.
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