**Solution:**

Let's start by understanding the given problem.

We are given three sums, a, b, and c, which represent the sums of p, q, and r terms respectively of an arithmetic progression (A.P). We need to find the value of the expression:

(a/p) (q-r) (b/q) (r-p) (c/r) (p-q)

To solve this problem, let's break it down step by step.

**Step 1: Find the common difference of the arithmetic progression (A.P).**

The sum of p terms, a, can be expressed as:

a = (p/2) * [2a + (p-1)d]

Where a is the first term of the A.P and d is the common difference.

Similarly, we can write the expressions for b and c:

b = (q/2) * [2a + (q-1)d]
c = (r/2) * [2a + (r-1)d]

Comparing the three expressions, we can see that the common difference d is the same for all three sums.

**Step 2: Simplify the given expression using the values of a, b, and c.**

Substituting the values of a, b, and c in the given expression, we get:

(a/p) (q-r) (b/q) (r-p) (c/r) (p-q) = [(p/2) * [2a + (p-1)d] / p] * (q - r) * [(q/2) * [2a + (q-1)d] / q] * (r - p) * [(r/2) * [2a + (r-1)d] / r] * (p - q)

**Step 3: Simplify further and combine like terms.**

Simplifying the expression, we get:

(a/p) (q-r) (b/q) (r-p) (c/r) (p-q) = (1/2) * [2a + (p-1)d] * (1/2) * [2a + (q-1)d] * (1/2) * [2a + (r-1)d] * (p - q) * (q - r) * (r - p)

= (1/8) * [(2a + (p-1)d) * (2a + (q-1)d) * (2a + (r-1)d)] * (p - q) * (q - r) * (r - p)

**Step 4: Simplify the expression further.**

Expanding the terms inside the brackets, we get:

(2a + (p-1)d) * (2a + (q-1)d) * (2a + (r-1)d) = 8a^3 + 4ad(p + q + r) + 2d^2(pq + qr + pr) - d^3(p + q + r)

Substituting this back into the expression and simplifying, we get:

(a/p) (q-r) (b/q) (r-p) (c/r) (p-q) = (1/8) * [8a^3 + 4ad(p + q + r) +