What happens to the interference pattern when we add more sources? Let's start by switching from two sources d apart to three sources d apart.
Do we still get maxima at the same angles where we got maxima for two sources?
Yes, the constructive interference equation d sin(θ) = mλ still applies, and applies for any number of sources separated by a distance d. Now we're simply adding three waves in phase instead of two, and for N sources we'd add N waves in phase.
Do we still get minima at the same angles where we got minima for two sources?
No. At the locations where the first two sources cancelled one another, they would still be cancelling one another but there would not be completely destructive interference taking place because there would be nothing to cancel the waves from the third source.
The destructive interference equation d sin(θ) = (m + 1/2) λ applies for two sources only.
For two sources there is one location between each interference maximum where destructive interference occurs. For instance, between the central maximum and the first-order maximum destructive interference occurs at a point 1/2 λ further from one source than the other.
For three sources there are two locations between each interference maximum where destructive interference occurs. Between the central maximum and the first-order maximum destructive interference occurs at points 1/3 λ and 2/3 λ further from one source than the next.
For N sources there are N-1 locations between each interference maximum where destructive interference occurs.