code: 
  
  
  
  def     UpperCAmelCase__ (							__snake_case							)   -> bool:
    if not isinstance(__snake_case						,				__snake_case							):
      raise ValueError('''Input series is not valid, valid series - [2, 4, 8]'''							)
    if len(__snake_case							) == 0:
      raise ValueError('''Input list must be a non empty list'''							)
    if len(__snake_case							) == 1:
      return True
    try:
      _A           =    series[1] / series[0]
      for index in range(len(__snake_case							) - 1							):
        if series[index + 1] / series[index] != common_ratio:
          return False
    except ZeroDivisionError:
      return False
    return True
  
  
  
  
  def     UpperCAmelCase__ (							__snake_case							)   -> float:
    if not isinstance(__snake_case						,				__snake_case							):
      raise ValueError('''Input series is not valid, valid series - [2, 4, 8]'''							)
    if len(__snake_case							) == 0:
      raise ValueError('''Input list must be a non empty list'''							)
    _A           =    1
    for value in series:
      answer *= value
    return pow(__snake_case						,				1 / len(__snake_case							)							)
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod()
style_context: 
  
  
  
  from ..utils import requires_backends
  
  
  __lowerCamelCase  				=					None
  
  
  
  class 		_snake_case      :
  
  
  
  
  
   """simple docstring"""
  
  
  
   def __init__(						self	,    *a	,    **a					)	->							Tuple:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     requires_backends(self	,    ['''detectron2''']					)
  
  
  
   @classmethod
   def lowercase_		(						cls	,    *a	,    **a					)	->							Optional[int]:
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     requires_backends(cls	,    ['''detectron2''']					)