The problem states that $(2x - 5), (x - 4), (-3x + 10)$ are the first three terms of a geometric sequence (barisan geometri). To find the integer value of $x$, we will use the property of geometric sequences, which is that the ratio between consecutive terms must be constant. This means:

$\frac{a_2}{a_1} = \frac{a_3}{a_2}$

Where:

• $a_1 = 2x - 5$
• $a_2 = x - 4$
• $a_3 = -3x + 10$

Now, let's set up the equation:

$\frac{x - 4}{2x - 5} = \frac{-3x + 10}{x - 4}$

I will solve this equation for $x$.The solutions to the equation are $x = 3$ and $x = \frac{22}{7}$. Since we are looking for the integer value of $x$, the correct solution is:

$x = 3$

Would you like further explanation or have any questions about this solution?

Here are 5 related questions you might find useful:

1. How do you derive the ratio formula for a geometric sequence?
2. Can geometric sequences have negative terms?
3. How would the problem change if it were an arithmetic sequence instead?
4. What is the general formula for the nth term of a geometric sequence?
5. How do you determine the common ratio of a geometric sequence?

Tip: Always check that your solutions satisfy the original problem, especially when solving for multiple values.