Question

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?(1 point)
Responses

8 3/4
8 Start Fraction 3 over 4 End Fraction

4 3/4
4 Start Fraction 3 over 4 End Fraction

8 1/4
8 Start Fraction 1 over 4 End Fraction

4 1/4

Answer 1

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

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

Now calculate it step by step:

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

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

3. Add this to \( \frac{1}{4} \):
\[
A_9 = \frac{1}{4} + 4
\]

Convert \( 4 \) to a fraction with a denominator of 4:
\[
4 = \frac{16}{4}
\]

Now add the fractions:
\[
A_9 = \frac{1}{4} + \frac{16}{4} = \frac{17}{4}
\]

Now convert \( \frac{17}{4} \) into a mixed number:
\[
\frac{17}{4} = 4 \frac{1}{4}
\]

The 9th term of the sequence is \( 4 \frac{1}{4} \).

So, the correct answer is **4 1/4**.