It's not to do with the number of carbons - its the number of hydrogens coming off the adjacent carbon, + 1 to the number and that gives you the amount of splitting in that peak.
If the adjacent carbon has 0 hydrogens, add 1 and you get 1. So the peak will just be a singlet and appear as a single line with no splitting.
If the adjacent carbon has 1 hydrogen, add one and you get 2. So the peak will split into 2, and is called a doublet.
Can someone explain this? HOW many adjacent carbons on singlet and doublets? Can you explain how to use the (n-1) rule?
if there are hydrogens bonded to adjacent carbon atoms then the peak will split into n+1 peaks where n is the number of hydrogens on the adjacent atoms. The ratio of peak heights is determined by Pascal's triangle.