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Answer :
Sure, let's take a look at the arithmetic sequence provided: 14, 24, 34, 44, 54, ...
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the "common difference."
To find the common difference, we can take the difference between any two consecutive terms. Let's use the first two terms:
1. The first term [tex]\( f(1) \)[/tex] is 14.
2. The second term [tex]\( f(2) \)[/tex] is 24.
Now, calculate the common difference:
[tex]\[ \text{Common difference} = f(2) - f(1) = 24 - 14 = 10. \][/tex]
With the common difference known, we can describe the recursive function for generating the sequence. A recursive function expresses each term in the sequence in terms of the previous term. The recursive formula for an arithmetic sequence is:
[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.
Using the common difference (10) and the first term (14), the recursive function is:
[tex]\[ f(n+1) = f(n) + 10 \][/tex]
where the initial term [tex]\( f(1) = 14 \)[/tex].
Therefore, the statement that correctly describes the recursive function for 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].
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the "common difference."
To find the common difference, we can take the difference between any two consecutive terms. Let's use the first two terms:
1. The first term [tex]\( f(1) \)[/tex] is 14.
2. The second term [tex]\( f(2) \)[/tex] is 24.
Now, calculate the common difference:
[tex]\[ \text{Common difference} = f(2) - f(1) = 24 - 14 = 10. \][/tex]
With the common difference known, we can describe the recursive function for generating the sequence. A recursive function expresses each term in the sequence in terms of the previous term. The recursive formula for an arithmetic sequence is:
[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.
Using the common difference (10) and the first term (14), the recursive function is:
[tex]\[ f(n+1) = f(n) + 10 \][/tex]
where the initial term [tex]\( f(1) = 14 \)[/tex].
Therefore, the statement that correctly describes the recursive function for 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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