Question 1184306
Here's how to determine the correct relationship between p, q, and r:

1. **Express the geometric sequence:**

Since a, b, and c are in a geometric sequence, we can write $b^2 = ac$.

2. **Express the given relationship:**

We are given that $ap = bq = cr$. Let's call this common value k. Then:
* $ap = k \Rightarrow a = \frac{k}{p}$
* $bq = k \Rightarrow b = \frac{k}{q}$
* $cr = k \Rightarrow c = \frac{k}{r}$

3. **Substitute into the geometric sequence equation:**

Substitute the expressions for a, b, and c into the equation $b^2 = ac$:

$(\frac{k}{q})^2 = (\frac{k}{p})(\frac{k}{r})$

$\frac{k^2}{q^2} = \frac{k^2}{pr}$

4. **Simplify:**

Since k is a positive real number, we can divide both sides by $k^2$:

$\frac{1}{q^2} = \frac{1}{pr}$

$q^2 = pr$

5. **Interpret the result:**

The equation $q^2 = pr$ means that p, q, and r are in a geometric sequence.

Therefore, the correct condition is that p, q, and r are in geometric sequence.

Final Answer: The final answer is $\boxed{A}$