The structure of 1-methoxypropane is CH₃-CH₂-CH₂-OCH₃
I will label the carbons A-D from left to right.
A B C D
CH₃-CH₂-CH₂-OCH₃
In a proton NMR spectrum, we are looking at the chemical shifts of each unique hydrogen atom, and the splitting patterns tell us how many hydrogens are attached to the adjacent carbon. Therefore, the signal from the protons on carbon A will be split by the protons on carbon B, and the signal for protons on carbon A will have a splitting pattern equal to n+1, where n = number of hydrogens on the adjacent carbon.
Therefore, for the protons on carbon A, there are two neighbouring protons and these will give a splitting patter of 3 peaks, also known as a triplet.
Protons on carbon A: 2 adjacent protons result in a triplet signal.
Protons on carbon B: 5 adjacent protons result in a sextet signal.
Protons on carbon C: 2 adjacent protons result in a triplet signal.
Protons on carbon D: 0 adjacent protons result in a singlet signal.