

from __future__ import annotations




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		)->		list[float | int]:



    """simple docstring"""






    if not all((nth_term, start_term_a, common_ratio_r)       ):
        return []
    UpperCamelCase_          =		[]
    UpperCamelCase_          =		1
    UpperCamelCase_          =		common_ratio_r
    for _ in range(int(lowercase_       )       ):
        if not series:
            series.append(lowercase_       )
        else:
            power += 1
            series.append(float(start_term_a * multiple       )       )
            UpperCamelCase_          =		pow(float(lowercase_       )       ,		lowercase_       )
    return series


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 SCREAMING_SNAKE_CASE						:Optional[Any]      =			float(input("""Enter the last number (n term) of the Geometric Series"""))
 SCREAMING_SNAKE_CASE						:List[str]      =			float(input("""Enter the starting term (a) of the Geometric Series"""))
 SCREAMING_SNAKE_CASE						:Optional[int]      =			float(
     input("""Enter the common ratio between two terms (r) of the Geometric Series""")
 )
 print("""Formula of Geometric Series => a + ar + ar^2 ... +ar^n""")
 print(geometric_series(nth_term, start_term_a, common_ratio_r))



from __future__ import annotations

from collections.abc import Generator



def    UpperCamelCase(					lowercase_							)	->				Generator[int, None, None]:





  '''simple docstring'''





  if not isinstance(lowercase_			,					lowercase_							) or n < 1:
    raise Exception("""Sequence only defined for positive integers"""							)

  yield n
  while n != 1:
    if n % 2 == 0:
      n //= 2
    else:
      snake_case_       						=      3 * n + 1
    yield n



def    UpperCamelCase(					)	->				Optional[int]:





  '''simple docstring'''





  snake_case_       						=      43
  snake_case_       						=      tuple(collatz_sequence(lowercase_							)							)
  print(lowercase_							)
  print(f'''Collatz sequence from {n} took {len(lowercase_							)} steps.'''							)


if __name__ == "__main__":
    main()