Answer
The path length difference $\Delta L$ increases.
Work Step by Step
We can write an expression for the path length difference:
$\Delta L = d~sin~\theta = m~\lambda$, where $m$ is an integer
If you move from one bright fringe in a two-slit interference pattern to the next one farther out, then $\theta$ increases and $m$ increases by 1.
Thus, the path length difference $\Delta L$ increases.
