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Answer :
We start with the arithmetic sequence:
[tex]$$
14, \; 24, \; 34, \; 44, \; 54, \; \ldots
$$[/tex]
An arithmetic sequence is defined by a constant difference between consecutive terms. To find the common difference, subtract the first term from the second term:
[tex]$$
d = 24 - 14 = 10
$$[/tex]
To confirm, we can check the next difference:
[tex]$$
34 - 24 = 10
$$[/tex]
Since every consecutive pair has the same difference, the common difference is indeed [tex]$10$[/tex].
The recursive function for an arithmetic sequence is given by:
[tex]$$
f(n+1) = f(n) + d
$$[/tex]
Substituting the common difference [tex]$d=10$[/tex], we have:
[tex]$$
f(n+1) = f(n) + 10
$$[/tex]
The first term is provided as [tex]$f(1)=14$[/tex].
Thus, the recursive function that generates the sequence is:
[tex]$$
f(n+1) = f(n) + 10 \quad \text{with} \quad f(1)=14.
$$[/tex]
This corresponds to option 3.
[tex]$$
14, \; 24, \; 34, \; 44, \; 54, \; \ldots
$$[/tex]
An arithmetic sequence is defined by a constant difference between consecutive terms. To find the common difference, subtract the first term from the second term:
[tex]$$
d = 24 - 14 = 10
$$[/tex]
To confirm, we can check the next difference:
[tex]$$
34 - 24 = 10
$$[/tex]
Since every consecutive pair has the same difference, the common difference is indeed [tex]$10$[/tex].
The recursive function for an arithmetic sequence is given by:
[tex]$$
f(n+1) = f(n) + d
$$[/tex]
Substituting the common difference [tex]$d=10$[/tex], we have:
[tex]$$
f(n+1) = f(n) + 10
$$[/tex]
The first term is provided as [tex]$f(1)=14$[/tex].
Thus, the recursive function that generates the sequence is:
[tex]$$
f(n+1) = f(n) + 10 \quad \text{with} \quad f(1)=14.
$$[/tex]
This corresponds to option 3.
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