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.
Let's calculate \( A_9 \):
\[ A_9 = \frac{1}{4} + (9 - 1) \cdot \frac{1}{2} \] \[ = \frac{1}{4} + 8 \cdot \frac{1}{2} \] \[ = \frac{1}{4} + 4 \] \[ = \frac{1}{4} + \frac{16}{4} \quad \text{(converting 4 to have a common denominator)} \] \[ = \frac{1 + 16}{4} \] \[ = \frac{17}{4} \]
Now let's examine the responses:
- 814
- 8 Start Fraction 1 over 4 End Fraction (which represents \( 8 \frac{1}{4} = \frac{33}{4} \))
- 434
- 4 Start Fraction 3 over 4 End Fraction (which represents \( 4 \frac{3}{4} = \frac{15}{4} \))
- 414
- 4 Start Fraction 1 over 4 End Fraction (which represents \( 4 \frac{1}{4} = \frac{17}{4} \))
- 834
The correct answer is 4 Start Fraction 1 over 4 End Fraction, which simplifies to \( \frac{17}{4} \).