To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = \frac{1}{4} + (n-1) \cdot 2 \), we need to substitute \( n = 9 \) into the formula.
Here's how to do it step by step:
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Substitute \( n = 9 \) into the formula: \[ A_9 = \frac{1}{4} + (9-1) \cdot 2 \]
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Calculate \( 9 - 1 \): \[ 9 - 1 = 8 \] So, we can rewrite the equation as: \[ A_9 = \frac{1}{4} + 8 \cdot 2 \]
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Calculate \( 8 \cdot 2 \): \[ 8 \cdot 2 = 16 \] Now we have: \[ A_9 = \frac{1}{4} + 16 \]
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Convert 16 to a fraction to combine with \( \frac{1}{4} \): \[ 16 = \frac{64}{4} \] So we can rewrite \( A_9 \) as: \[ A_9 = \frac{1}{4} + \frac{64}{4} \]
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Combine the fractions: \[ A_9 = \frac{1 + 64}{4} = \frac{65}{4} \]
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Convert \( \frac{65}{4} \) to a mixed number: \[ \frac{65}{4} = 16 \frac{1}{4} \]
However, it seems there was confusion in your mention of \( 4 \frac{1}{4} \); the correct answer for \( A_9 \) is \( 16 \frac{1}{4} \) or \( 16.25 \) depending on how you want to express the answer.
So the correct answer for the 9th term using the formula is 16.25 or 16 \frac{1}{4}. If you were told it's \( 4 \frac{1}{4} \), that appears to be incorrect for this calculation.