Formulas for Sequences Quick Check

Question

Question

Which of the following correctly uses the explicit formula, A^n=1/4+(n-1)*1/2, to find the 9th term of the described arithmetic sequence? (1 point)
Responses

4 3/4

8 3/4

4 1/4

8 1/4

Answer 1

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.

1. Substitute \( n = 9 \):

   \[ A^9 = \frac{1}{4} + (9-1) \cdot \frac{1}{2} \]

2. Calculate \( (9-1) \):

   \[ (9-1) = 8 \]

3. Now substitute that value into the formula:

   \[ A^9 = \frac{1}{4} + 8 \cdot \frac{1}{2} \]

4. Calculate \( 8 \cdot \frac{1}{2} \):

   \[ 8 \cdot \frac{1}{2} = 4 \]

5. Now add it to \( \frac{1}{4} \):

   \[ A^9 = \frac{1}{4} + 4 = \frac{1}{4} + \frac{16}{4} = \frac{17}{4} \]

6. To convert \( \frac{17}{4} \) into a mixed number:

   \[ \frac{17}{4} = 4 \frac{1}{4} \]

So, the 9th term \( A^9 \) is \( 4 \frac{1}{4} \).

Therefore, the correct response is:

4 1/4