To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = \frac{1}{4} + (n - 1) \cdot \frac{1}{2} \), we need to substitute \( n = 9 \) into the formula.
Here’s how we can calculate it step by step:
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Replace \( n \) with 9 in the formula: \[ A_9 = \frac{1}{4} + (9 - 1) \cdot \frac{1}{2} \]
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Simplify the equation: \[ A_9 = \frac{1}{4} + 8 \cdot \frac{1}{2} \]
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Calculate \( 8 \cdot \frac{1}{2} \): \[ 8 \cdot \frac{1}{2} = 4 \]
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Now substitute back into the equation: \[ A_9 = \frac{1}{4} + 4 \]
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Convert 4 into a fraction with a denominator of 4 to add: \[ 4 = \frac{16}{4} \]
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Now add: \[ A_9 = \frac{1}{4} + \frac{16}{4} = \frac{17}{4} \]
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Convert \( \frac{17}{4} \) into a mixed number: \[ \frac{17}{4} = 4 \frac{1}{4} \]
So, the 9th term is \( 4 \frac{1}{4} \).
The correct response is: 4 1/4 (4 Start Fraction 1 over 4 End Fraction).