To describe the recursive function used to generate the given arithmetic sequence, let's identify two key components: the first term (initial term) and the common difference.
The sequence provided is:
[tex]\[ 14, 24, 34, 44, 54, \ldots \][/tex]
1. Identifying the Initial Term:
The first term in the sequence is [tex]\(14\)[/tex].
2. Identifying the Common Difference:
To find the common difference, we subtract the first term from the second term:
[tex]\[ 24 - 14 = 10 \][/tex]
Thus, each term is obtained by adding [tex]\(10\)[/tex] to the previous term.
With this information, we can define the recursive function for the arithmetic sequence. The initial term is [tex]\(14\)[/tex] and the common difference is [tex]\(10\)[/tex].
Therefore, the correct statement describing the recursive function is:
The common difference is [tex]\(10\)[/tex], so the function is [tex]\( f(n+1) = f(n) + 10 \)[/tex] where [tex]\( f(1) = 14 \)[/tex].
