Answer :
To solve the problem of identifying the recursive function used to generate the given arithmetic sequence, we need to first understand the characteristics of an arithmetic sequence. An arithmetic sequence has a constant difference between consecutive terms, known as the common difference.
Here’s how we can determine the correct recursive function statement:
1. Identify the given sequence:
The sequence provided is: 14, 24, 34, 44, 54, ...
2. Determine the common difference:
To find the common difference, subtract the first term from the second term:
[tex]\[
24 - 14 = 10
\][/tex]
This indicates that each term in the sequence increases by 10 from the previous term.
3. Identify the first term:
The first term of the sequence is 14.
4. Choose the correct recursive function:
Now, we need to find the statement that correctly describes this sequence using its first term and common difference. The recursive formula for an arithmetic sequence can be expressed as [tex]\( f(n+1) = f(n) + d \)[/tex], where [tex]\( d \)[/tex] is the common difference and [tex]\( f(1) \)[/tex] is the first term.
Given our findings:
- The common difference is 10.
- The first term is 14.
The correct statement is:
The common difference is 10, so the function is [tex]\( f(n+1) = f(n) + 10 \)[/tex] where [tex]\( f(1) = 14 \)[/tex].
This recursive function accurately describes the way each term in the sequence is generated by adding 10 to the previous term, starting from the first term of 14.
Here’s how we can determine the correct recursive function statement:
1. Identify the given sequence:
The sequence provided is: 14, 24, 34, 44, 54, ...
2. Determine the common difference:
To find the common difference, subtract the first term from the second term:
[tex]\[
24 - 14 = 10
\][/tex]
This indicates that each term in the sequence increases by 10 from the previous term.
3. Identify the first term:
The first term of the sequence is 14.
4. Choose the correct recursive function:
Now, we need to find the statement that correctly describes this sequence using its first term and common difference. The recursive formula for an arithmetic sequence can be expressed as [tex]\( f(n+1) = f(n) + d \)[/tex], where [tex]\( d \)[/tex] is the common difference and [tex]\( f(1) \)[/tex] is the first term.
Given our findings:
- The common difference is 10.
- The first term is 14.
The correct statement is:
The common difference is 10, so the function is [tex]\( f(n+1) = f(n) + 10 \)[/tex] where [tex]\( f(1) = 14 \)[/tex].
This recursive function accurately describes the way each term in the sequence is generated by adding 10 to the previous term, starting from the first term of 14.
