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

834
8 Start Fraction 3 over 4 End Fraction

434
4 Start Fraction 3 over 4 End Fraction

414
4 Start Fraction 1 over 4 End Fraction

814

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:

\[
A_9 = \frac{1}{4} + (9-1) \cdot \frac{1}{2}
\]
\[
A_9 = \frac{1}{4} + 8 \cdot \frac{1}{2}
\]
\[
A_9 = \frac{1}{4} + 4
\]
Now, we need to express 4 as a fraction with a denominator of 4:

\[
4 = \frac{16}{4}
\]
Now, we can add:

\[
A_9 = \frac{1}{4} + \frac{16}{4} = \frac{17}{4}
\]

Now, let’s convert \( \frac{17}{4} \) into a mixed number:

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

So, the 9th term of the sequence \( A_9 \) is \( 4 \frac{1}{4} \).

Therefore, the correct answer is:

**414** \(4 \frac{1}{4}\)