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

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

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

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

8 1/4

Answer 1

To find the 9th term using the explicit formula for the arithmetic sequence, we can substitute \( n = 9 \) into the formula:

\[
A_n = \frac{1}{4} + (n - 1) \cdot \frac{1}{2}
\]

Substituting \( n = 9 \):

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

This simplifies to:

\[
A_9 = \frac{1}{4} + 8 \cdot \frac{1}{2}
\]
\[
= \frac{1}{4} + 4
\]
\[
= \frac{1}{4} + \frac{16}{4}
\]
\[
= \frac{17}{4}
\]

Now we convert \(\frac{17}{4}\) to a mixed number:

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

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

Among the responses you provided, the correct answer is:

**4 1/4**