Introduction:
If a, b, and c are in arithmetic progression, it means that the difference between consecutive terms is constant. In other words, the common difference between a and b is the same as the common difference between b and c.

Possible Combinations:
When considering the terms a, b, and c, there are three possible combinations: a b, b c, and c a. Let's examine each combination in detail.

Combination: a b
In this combination, a comes before b. Since a, b, and c are in arithmetic progression, we can write their respective values as a, a + d, and a + 2d, where d represents the common difference.

If we substitute these values into the combination a b, we get a (a + d). Simplifying it further, we obtain a^2 + ad.

Combination: b c
In this combination, b comes before c. Using the same approach, we can express the values of b and c as a + d and a + 2d, respectively.

If we substitute these values into the combination b c, we get (a + d) (a + 2d). Expanding this expression, we have a^2 + 3ad + 2d^2.

Combination: c a
In this combination, c comes before a. Similarly, we can represent the values of c and a as a + 2d and a, respectively.

Substituting these values into the combination c a, we obtain (a + 2d) a. Expanding it further, we have a^2 + 2ad.

Summary:
In summary, the combinations a b, b c, and c a can be represented as:
- a b: a^2 + ad
- b c: a^2 + 3ad + 2d^2
- c a: a^2 + 2ad

These expressions demonstrate the relationships between the terms in an arithmetic progression when considering different combinations.

If d=0