1. **State the problem:** We are given two points from a sequence plotted on a graph: $(1, -3)$ and $(2, -\frac{3}{2})$. We want to find the formula for the geometric sequence $a_n$ that these points represent. 2. **Recall the formula for a geometric sequence:** $$a_n = a_1 r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 3. **Use the given points to find $a_1$ and $r$:** - From the point $(1, -3)$, we know $a_1 = -3$. - From the point $(2, -\frac{3}{2})$, we have: $$a_2 = a_1 r = -\frac{3}{2}$$ Substitute $a_1 = -3$: $$-3 r = -\frac{3}{2}$$ 4. **Solve for $r$:** $$r = \frac{-\frac{3}{2}}{-3} = \frac{3/2}{3} = \frac{1}{2}$$ 5. **Write the formula for the sequence:** $$a_n = -3 \left(\frac{1}{2}\right)^{n-1}$$ 6. **Interpretation:** The sequence starts at $-3$ and each term is half the previous term, so the points given fit a geometric sequence with ratio $\frac{1}{2}$. **Final answer:** $$a_n = -3 \left(\frac{1}{2}\right)^{n-1}$$