Question

Which arithmetic sequence is described by the linear function f(n)=1/2n−13
?(1 point)
Responses

−13,−25/2,−12 . . .

27/2,14,29/2 . . .

−25/2,−12,−23/2 . . .

−25/2,−23/2,−21/2 . . .

Answer 1

The given linear function is \( f(n) = \frac{1}{2}n - 13 \). To identify which arithmetic sequence it describes, we can calculate \( f(n) \) for the first few values of \( n \).

1. **For \( n = 1 \)**:
\[
f(1) = \frac{1}{2} \cdot 1 - 13 = \frac{1}{2} - 13 = \frac{1}{2} - \frac{26}{2} = -\frac{25}{2}
\]

2. **For \( n = 2 \)**:
\[
f(2) = \frac{1}{2} \cdot 2 - 13 = 1 - 13 = 1 - \frac{26}{2} = -\frac{12}{2} = -12
\]

3. **For \( n = 3 \)**:
\[
f(3) = \frac{1}{2} \cdot 3 - 13 = \frac{3}{2} - 13 = \frac{3}{2} - \frac{26}{2} = -\frac{23}{2}
\]

Putting these results together, we have:
- \( f(1) = -\frac{25}{2} \)
- \( f(2) = -12 \)
- \( f(3) = -\frac{23}{2} \)

Now, we can write the sequence up to the first three terms:
\[
-\frac{25}{2}, -12, -\frac{23}{2}
\]

Among the choices provided, the sequence that matches this result is:

**−25/2,−12,−23/2 . . .**