To find the 9th term of the arithmetic sequence using the given explicit formula \( A_n = 14 + (n - 1) \cdot 12 \), we need to substitute \( n = 9 \) into the formula.
\[ A_9 = 14 + (9 - 1) \cdot 12 \]
Calculate \( (9 - 1) \):
\[ 9 - 1 = 8 \]
Now substitute this back into the formula:
\[ A_9 = 14 + 8 \cdot 12 \]
Calculate \( 8 \cdot 12 \):
\[ 8 \cdot 12 = 96 \]
Now add this to 14:
\[ A_9 = 14 + 96 = 110 \]
Now, let's compare this result with the given options to see if any of them match:
- 434
- 814
- 414
- 834
None of the options match the value of 110, so it seems like none of the responses are correct in this case. However, it might be worth checking if there were any misinterpretations in the content of the responses. If the terms or values changed, we could adjust accordingly.
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