1. **State the problem:** We have an arithmetic sequence with the first three terms: 7, 5, and $1 - 3x$. We need to find the value of $x$ and the next term in the sequence. 2. **Recall the formula for an arithmetic sequence:** The difference between consecutive terms is constant. This means: $$a_2 - a_1 = a_3 - a_2$$ where $a_1$, $a_2$, and $a_3$ are the first, second, and third terms respectively. 3. **Apply the formula:** $$5 - 7 = (1 - 3x) - 5$$ 4. **Simplify both sides:** $$-2 = 1 - 3x - 5$$ $$-2 = -4 - 3x$$ 5. **Isolate $x$:** Add 4 to both sides: $$-2 + 4 = -4 - 3x + 4$$ $$2 = -3x$$ 6. **Divide both sides by -3:** $$\frac{2}{\cancel{-3}} = \frac{-3x}{\cancel{-3}}$$ $$-\frac{2}{3} = x$$ 7. **Find the next term ($a_4$):** The common difference $d$ is: $$d = a_2 - a_1 = 5 - 7 = -2$$ The fourth term is: $$a_4 = a_3 + d = (1 - 3x) + (-2)$$ Substitute $x = -\frac{2}{3}$: $$a_4 = 1 - 3\left(-\frac{2}{3}\right) - 2 = 1 + 2 - 2 = 1$$ **Final answers:** - $x = -\frac{2}{3}$ - The next term in the sequence is $1$.