(f) \( \quad x-5 ; 2 x-4 ; 6 x \) are the first three terms of a geometric sequence. De value(s) of \( x \).

In a geometric sequence, the ratio of consecutive terms is constant. So, we can set up the equation by comparing the ratios of the first two terms and the last two terms: \[ \frac{2x - 4}{x - 5} = \frac{6x}{2x - 4} \] Cross-multiplying gives: \[ (2x - 4)(2x - 4) = 6x(x - 5) \] Expanding both sides leads to a quadratic equation. Solving this quadratic will yield the values of \( x \). Considering some troubleshooting tips, when checking for errors, ensure you've correctly expanded and simplified each axis in the equation. Watch out for negative signs and factor carefully if the quadratic seems unyielding; it's easy to misplace a term in the process!