1. **State the problem:** We have an arithmetic sequence defined by the rule $x_n = an + b$, where $a$ and $b$ are constants. We need to find $a$ and $b$ given the sequence terms: $\frac{3}{5}, 1, \frac{7}{5}, \frac{9}{5}, \frac{11}{5}, \ldots$ 2. **Recall the formula for an arithmetic sequence:** $$x_n = a n + b$$ where $a$ is the common difference (the amount added each time) and $b$ is the first term when $n=1$. 3. **Identify terms:** - $x_1 = \frac{3}{5}$ - $x_2 = 1 = \frac{5}{5}$ - $x_3 = \frac{7}{5}$ 4. **Use the formula for $n=1$:** $$x_1 = a(1) + b = a + b = \frac{3}{5}$$ 5. **Use the formula for $n=2$:** $$x_2 = a(2) + b = 2a + b = 1 = \frac{5}{5}$$ 6. **Subtract the first equation from the second to eliminate $b$:** $$\cancel{2a} + b - (\cancel{a} + b) = \frac{5}{5} - \frac{3}{5}$$ $$2a - a = \frac{2}{5}$$ $$a = \frac{2}{5}$$ 7. **Substitute $a$ back into the first equation to find $b$:** $$\frac{2}{5} + b = \frac{3}{5}$$ $$b = \frac{3}{5} - \frac{2}{5} = \frac{1}{5}$$ **Final answer:** $$a = \frac{2}{5}, \quad b = \frac{1}{5}$$