1. **Stating the problem:** We are given three terms of a sequence: $x - 1$, $2x$, and $4x - 3$. We need to find the value of $x$ such that these terms form an arithmetic progression (AP). 2. **Formula and rule for arithmetic progression:** In an AP, the difference between consecutive terms is constant. This means: $$2x - (x - 1) = (4x - 3) - 2x$$ 3. **Set up the equation:** Simplify both sides: $$2x - x + 1 = 4x - 3 - 2x$$ $$x + 1 = 2x - 3$$ 4. **Solve for $x$:** $$x + 1 = 2x - 3$$ $$1 + 3 = 2x - x$$ $$4 = x$$ 5. **Verify the terms with $x=4$:** - First term: $4 - 1 = 3$ - Second term: $2 \times 4 = 8$ - Third term: $4 \times 4 - 3 = 16 - 3 = 13$ 6. **Check if these form an AP:** - Difference between second and first: $8 - 3 = 5$ - Difference between third and second: $13 - 8 = 5$ Since the differences are equal, the terms form an arithmetic progression. **Final answer:** The terms are $3, 8, 13$, which corresponds to option c.