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 substitute \( n = 9 \) into the formula.
Starting with the formula: \[ A_n = \frac{1}{4} + (n - 1) \cdot \frac{1}{2} \]
Substituting \( n = 9 \): \[ A_9 = \frac{1}{4} + (9 - 1) \cdot \frac{1}{2} \]
Calculating \( (9 - 1) \): \[ A_9 = \frac{1}{4} + 8 \cdot \frac{1}{2} \]
Calculating \( 8 \cdot \frac{1}{2} \): \[ A_9 = \frac{1}{4} + 4 \]
Now, converting \( 4 \) into a fraction: \[ 4 = \frac{16}{4} \]
Adding the fractions: \[ A_9 = \frac{1}{4} + \frac{16}{4} = \frac{17}{4} \]
Thus, the 9th term of the arithmetic sequence is: \[ A_9 = \frac{17}{4} \]