A homologous series is a class that can be represented by a general formula.
Below are a few general formulae. They are all assumed to have one functional group.
The restrictions on n are necessary since the smallest allowable value for n would represent the smallest compound in that series.
As an example, the smallest ester would need TWO carbons, hence n would start at 2, but the smallest acid can have 1 carbon, and n would start at 1. etc.
Alkane:
CnH2n+2 (n=1,2,3..)
Cycloalkane:
CnH2n (n=3,4,5...)
Alkene:
CnH2n (n=2,3,4...)
Alkyne:
CnH2n-2 (n=2,,3,4...)
Alcohol:
CnH2n+2O or CnH2n+1OH (n=1,2,3...)
Acid:
CnH2nO2 (n=1,2,3...)
Ester:
CnH2nO2 (n=2,3,4...)
Amine:
CnH2n+3N (n=1,2,3...)
Amide:
CnH2n+1NO (n=1,2,3...)
Aldehyde:
CnH2nO (n=1,2,3...)
Ketone:
CnH2nO (n=3,4,5...)