code: 
  
  
  '''simple docstring'''
  
  
  
  
  def 							a_       (						lowercase    )			->bool:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				if not isinstance(a_							,						a_    ):
  								raise ValueError("Input series is not valid, valid series - [2, 4, 8]"    )
  				if len(a_    ) == 0:
  								raise ValueError("Input list must be a non empty list"    )
  				if len(a_    ) == 1:
  								return True
  				try:
  								__lowerCamelCase		:      str											=					series[1] / series[0]
  								for index in range(len(a_    ) - 1    ):
  												if series[index + 1] / series[index] != common_ratio:
  																return False
  				except ZeroDivisionError:
  								return False
  				return True
  
  
  
  
  
  def 							a_       (						lowercase    )			->float:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				if not isinstance(a_							,						a_    ):
  								raise ValueError("Input series is not valid, valid series - [2, 4, 8]"    )
  				if len(a_    ) == 0:
  								raise ValueError("Input list must be a non empty list"    )
  				__lowerCamelCase		:      Tuple											=					1
  				for value in series:
  								answer *= value
  				return pow(a_							,						1 / len(a_    )    )
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  
  
  
  
  
style_context: 
  
  
  '''simple docstring'''
  
  
  
  
  def 							a_       (						lowercase    )			->str:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				return " ".join(sorted(set(sentence.split()    )    )    )
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  
  
  
  
  