Theory:

A homologous series is a group or class of organic compounds that have the same general formula and similar chemical properties but differ by a \(-CH_2\) group.
 
Consider the members of the alkanes listed in the below table. The following are their condensed structural formulas:
 
Name
Molecular
formula
Methane\(CH_4\)
Ethane\(CH_3CH_3\)
Propane\(CH_3CH_2CH3\)
Butane\(CH_3(CH_2)_2CH3\)
Pentane\(CH_3(CH_2)_3CH3\)
 
If you look at the preceding series, each successive member has one more methylene group than the preceding member, which is why they are called homologs.
 
Characteristics of homologous series:
  
1. Each member of the series differs from the previous or succeeding member by one methylene group (\(–CH_2\)) and thus by \(14 amu\) in molecular mass.
 
For example the homologous series of alcohol,
 
Name
Molecular
formula
Methanol\(CH_3OH\)
Ethanol\(CH_3CH_2OH\)
Propanol\(CH_3(CH_2)_2OH\)
Butanol\(CH_3(CH_2)_3OH\)
Pentanol\(CH_3(CH_2)_4OH\)
 
2. A homologous series members share the same elements and functional group.
 
For example the homologous series of carboxylic acid,
Name
Molecular
formula
Methanoic acid\(HCOOH\)
Ethanoic acid\(CH_3COOH\)
Propanoic acid\(CH_3CH_2COOH\)
Butanoic acid\(CH_3(CH_2)_2COOH\)
Pentanoic acid\(CH_3(CH_2)_3COOH\)
 
3. A general molecular formula is used to represent them.
Example:
For example, alkanes (\(C_nH_{2n + 2}\)), alkenes (\(C_nH_{2n}\)) and alkynes (\(C_nH_{2n – 2}\)).
4. Members of each homologous series exhibit a regular gradation in physical properties as their molecular mass increases.
Example:
For example, alkanes group compounds have weak Van Der Waals force.
5. Members of a homologous series have similar chemical properties.
Example:
For example, all alkanes on reaction with oxygen produce carbon dioxide, water with energy liberation.
6. A common method can be used to prepare all of the members in a homologous series.
Example:
For example, aldehydes can be prepared by oxidising primary alcohol.
\(RCH_2OH\xrightarrow{K_2Cr_2O_7} R-CHO\)