1. **State the problem:** We have an arithmetic sequence with values given for $n=3,5,7$ as $a_3=85$, $a_5=95$, and $a_7=105$. We want to find the linear function $f(x) = a_0 + d x$ where $a_0$ is the initial value at $n=0$ and $d$ is the common difference. 2. **Recall the formula for an arithmetic sequence:** $$a_n = a_0 + d n$$ where $a_0$ is the first term and $d$ is the common difference. 3. **Find the common difference $d$:** Using $a_3=85$ and $a_5=95$: $$d = \frac{a_5 - a_3}{5 - 3} = \frac{95 - 85}{2} = \frac{10}{2} = 5$$ 4. **Find $a_0$ using $a_3=85$ and $d=5$:** $$a_3 = a_0 + 3d$$ $$85 = a_0 + 3 \times 5$$ $$85 = a_0 + 15$$ $$a_0 = 85 - 15 = 70$$ 5. **Write the linear function:** $$f(x) = 70 + 5x$$ 6. **Check with other points:** For $n=5$, $$f(5) = 70 + 5 \times 5 = 70 + 25 = 95$$ For $n=7$, $$f(7) = 70 + 5 \times 7 = 70 + 35 = 105$$ Both match the given values. **Final answer:** The correct function is $f(x) = 70 + 5x$, which corresponds to option A.