To identify the recursive function for the sequence 41, 29, 17, 5..., let's observe the differences between consecutive terms:
- 41 to 29: \( 41 - 29 = 12 \)
- 29 to 17: \( 29 - 17 = 12 \)
- 17 to 5: \( 17 - 5 = 12 \)
It appears that each term is obtained by subtracting 12 from the previous term. Therefore, we can summarize this with a recursive formula.
The recursive formula is:
\[ A_n = A_{n-1} - 12 \]
Given that the first term (A1) is 41, we can summarize the recursive function as:
- Recursive Function: \( A_n = A_{n-1} - 12 \) with \( A_1 = 41 \)
This matches the option you provided as:
\[ A_n = A_{n-1} - 12, 41 \]
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