



'''simple docstring'''

from __future__ import annotations

from collections.abc import Generator







def     __UpperCamelCase					(				_lowercase       )			->      Optional[Any]:


	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:
			_lowercase       :							Optional[int]  	=		3 * n + 1
		yield n







def     __UpperCamelCase					(				)			->      Optional[Any]:
	_lowercase       :							Tuple  	=		43
	_lowercase       :							Tuple  	=		tuple(collatz_sequence(_lowercase       )       )
	print(_lowercase       )
	print(f'''Collatz sequence from {n} took {len(_lowercase       )} steps.'''       )


if __name__ == "__main__":
		main()


from __future__ import annotations




def 		A						(  SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						):




			"""simple docstring"""


			if not all((nth_term, start_term_a, common_ratio_r)							):
						return []
			UpperCAmelCase__		:list[float | int] 		=    []
			UpperCAmelCase__		:str 		=    1
			UpperCAmelCase__		:Any 		=    common_ratio_r
			for _ in range(int(SCREAMING_SNAKE_CASE							)							):
						if not series:
									series.append(SCREAMING_SNAKE_CASE							)
						else:
									power += 1
									series.append(float(start_term_a * multiple							)							)
									UpperCAmelCase__		:str 		=    pow(float(SCREAMING_SNAKE_CASE							)     ,						SCREAMING_SNAKE_CASE							)
			return series


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						__snake_case					:							Optional[int]           =							float(input('Enter the last number (n term) of the Geometric Series'))
						__snake_case					:							List[str]           =							float(input('Enter the starting term (a) of the Geometric Series'))
						__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))





