Given that (1)/(a), (1)/(b), (1)/(c) are in A.P., we can write:

If three terms $x, y, z$ are in A.P., then the middle term is the average of the other two, or equivalently, the common difference between consecutive terms is constant. This means $y - x = z - y$, which simplifies to $2y = x + z$.

property to the given terms.
Given that $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in A.P., we can write:

Simplify the right side by finding a common denominator:

The common difference, $d$, can be found by subtracting any term from its succeeding term. Let's use the first two terms:

From Step 2, we have $\frac{2}{b} = \frac{c+a}{ac}$. This means $\frac{1}{b} = \frac{c+a}{2ac}$.
Substitute this expression for $\frac{1}{b}$ into the equation for $d$:

To subtract these fractions, find a common denominator, which is $2ac$:

Combine the numerators:

Thus, the common difference is $\frac{a-c}{2ac}$.