The pattern of numbers below is an arithmetic sequence:

14, 24, 34, 44, 54, ...

Which statement describes the recursive function used to generate the sequence?

A. The common difference is 1, so the function is [tex]f(n+1) = f(n) + 1[/tex] where [tex]f(1) = 14[/tex].
B. The common difference is 4, so the function is [tex]f(n+1) = f(n) + 4[/tex] where [tex]f(1) = 10[/tex].
C. The common difference is 10, so the function is [tex]f(n+1) = f(n) + 10[/tex] where [tex]f(1) = 14[/tex].
D. The common difference is 14, so the function is [tex]f(n+1) = f(n) + 14[/tex] where [tex]f(1) = 10[/tex].

The pattern of numbers forms an arithmetic sequence with a common difference of 10. The recursive function used to generate the sequence is f(n-1) = f(n) - 10, where f(1) = 14.

Explanation:

The pattern of numbers given, 14, 24, 34, 44, 54, ... is an arithmetic sequence. In an arithmetic sequence, the common difference between consecutive terms remains constant. The common difference can be found by subtracting any two consecutive terms in the sequence. Here, if we subtract 14 from 24 or 24 from 34, we get a difference of 10. Therefore, the correct statement that describes the recursive function used to generate the sequence is: the common difference is 10, so the function is f(n-1) = f(n) - 10, where f(1) = 14.

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