To determine the recursive function and the first term \( A_1 \) of the sequence \( 41, 29, 17, 5 \), we can analyze the differences between consecutive terms.
- The difference between 41 and 29 is \( 41 - 29 = 12 \)
- The difference between 29 and 17 is \( 29 - 17 = 12 \)
- The difference between 17 and 5 is \( 17 - 5 = 12 \)
It seems that each term in the sequence decreases by 12. This suggests that the recursive relation is:
\[ A_n = A_{n-1} - 12 \]
Now, let's find the first term \( A_1 \).
From the given sequence:
- For \( n=4 \): \( A_4 = 5 \)
- For \( n=3 \): \( A_3 = A_4 + 12 = 5 + 12 = 17 \)
- For \( n=2 \): \( A_2 = A_3 + 12 = 17 + 12 = 29 \)
- For \( n=1 \): \( A_1 = A_2 + 12 = 29 + 12 = 41 \)
Based on this analysis:
The recursive function is: \[ A_n = A_{n-1} - 12 \]
with \( A_1 = 41 \).
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