Question

For the 3rd dark fringe's path position, the slit should be thought to be divided into how many parts? ___

Answer 1

Hey, you must have recognised the pattern by now. For the 3rd minima (dark fringe), divide the slit into 6 parts, such that each part has a path difference of $\lambda /2$. So, you will get $\frac{a\sin \theta }{6}=\frac{\lambda }{2}$ or $a\sin \theta =3\lambda$.