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Answer :
To solve this problem, we'll first identify the common difference in the given arithmetic sequence and then determine which statement correctly describes the recursive function to generate this sequence.
The sequence provided is: 14, 24, 34, 44, 54, ...
1. Identify the common difference:
- To find the common difference, subtract the first term from the second term.
- Second term: 24
- First term: 14
- Common difference = 24 - 14 = 10
2. Determine the recursive function:
- In an arithmetic sequence, each term is generated by adding the common difference to the previous term.
- We start with the first term, [tex]\( f(1) = 14 \)[/tex].
- Since the common difference is 10, the recursive function to generate the sequence is:
[tex]\[
f(n+1) = f(n) + 10 \quad \text{where} \quad f(1) = 14
\][/tex]
Hence, 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].
The sequence provided is: 14, 24, 34, 44, 54, ...
1. Identify the common difference:
- To find the common difference, subtract the first term from the second term.
- Second term: 24
- First term: 14
- Common difference = 24 - 14 = 10
2. Determine the recursive function:
- In an arithmetic sequence, each term is generated by adding the common difference to the previous term.
- We start with the first term, [tex]\( f(1) = 14 \)[/tex].
- Since the common difference is 10, the recursive function to generate the sequence is:
[tex]\[
f(n+1) = f(n) + 10 \quad \text{where} \quad f(1) = 14
\][/tex]
Hence, 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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