In the exponential function \( f(x) = 100(1.25)^{x-1} \), the expression \( 1.25 \) represents the common ratio. This is because in exponential functions of the form \( f(x) = a \cdot r^{x} \), the term \( r \) is the base that dictates the multiplicative factor by which the function grows or decays for each unit increase in \( x \).
Thus, the common ratio in the equation is 1.25.