Which of the following correctly uses the explicit formula, An=1/4+(n−1)⋅1/2 , to find the 9th term of the described arithmetic sequence?

Answer 1

To find the 9th term of the arithmetic sequence using the given explicit formula \( A_n = \frac{1}{4} + (n - 1) \cdot \frac{1}{2} \), we will substitute \( n = 9 \) into the formula.

1. Substitute \( n \) with \( 9 \): \[ A_9 = \frac{1}{4} + (9 - 1) \cdot \frac{1}{2} \]

2. Simplify \( (9 - 1) \): \[ A_9 = \frac{1}{4} + 8 \cdot \frac{1}{2} \]

3. Calculate \( 8 \cdot \frac{1}{2} \): \[ 8 \cdot \frac{1}{2} = 4 \]

4. Now substitute back: \[ A_9 = \frac{1}{4} + 4 \]

5. Convert \( 4 \) into a fraction with a common denominator of 4: \[ 4 = \frac{16}{4} \]

6. Add the two fractions: \[ A_9 = \frac{1}{4} + \frac{16}{4} = \frac{17}{4} \]

Therefore, the 9th term of the arithmetic sequence is \( \frac{17}{4} \).