Question

Which of the following correctly uses the explicit formula, An = 1/4 + (n-1) x 1/2, to find the 9th term of the described arithmetic sequence?(1 point)
8 3/4
4 1/4
4 3/4
8 1/4

Answer 1

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

\[
A_9 = \frac{1}{4} + (9-1) \times \frac{1}{2}
\]

Calculating this step-by-step:

1. Calculate \( (9-1) \):
\[
9-1 = 8
\]

2. Now multiply by \( \frac{1}{2} \):
\[
8 \times \frac{1}{2} = 4
\]

3. Now add \( \frac{1}{4} \):
\[
A_9 = \frac{1}{4} + 4
\]

To add these, convert 4 to a fraction with a denominator of 4:
\[
4 = \frac{16}{4}
\]

Now combine them:
\[
A_9 = \frac{1}{4} + \frac{16}{4} = \frac{17}{4}
\]

Convert \( \frac{17}{4} \) to a mixed number:
\[
\frac{17}{4} = 4 \frac{1}{4}
\]

Thus, the 9th term of the sequence is **4 1/4**.

The correct answer is **4 1/4**.