
"""simple docstring"""




from __future__ import annotations

def __snake_case (      UpperCamelCase						,					UpperCamelCase						,					UpperCamelCase						,					)       ->    list[float | int]:


		"""simple docstring"""





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


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					__lowerCAmelCase							:  Optional[int] 				=		float(input('''Enter the last number (n term) of the Geometric Series'''))
					__lowerCAmelCase							:  Dict 				=		float(input('''Enter the starting term (a) of the Geometric Series'''))
					__lowerCAmelCase							:  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))






"""simple docstring"""




def __snake_case (      UpperCamelCase    )       ->    float:


		"""simple docstring"""





		return -num if num < 0 else num

def __snake_case (      UpperCamelCase    )       ->    int:


		"""simple docstring"""





		if len(UpperCamelCase    ) == 0:
				raise ValueError('''abs_min() arg is an empty sequence'''    )
		a__   		=     x[0]
		for i in x:
				if abs_val(UpperCamelCase    ) < abs_val(UpperCamelCase    ):
						a__   		=     i
		return j

def __snake_case (      UpperCamelCase    )       ->    int:


		"""simple docstring"""





		if len(UpperCamelCase    ) == 0:
				raise ValueError('''abs_max() arg is an empty sequence'''    )
		a__   		=     x[0]
		for i in x:
				if abs(UpperCamelCase    ) > abs(UpperCamelCase    ):
						a__   		=     i
		return j

def __snake_case (      UpperCamelCase    )       ->    int:


		"""simple docstring"""





		if len(UpperCamelCase    ) == 0:
				raise ValueError('''abs_max_sort() arg is an empty sequence'''    )
		return sorted(UpperCamelCase						,					key=UpperCamelCase    )[-1]

def __snake_case (      )       ->    Optional[int]:


		"""simple docstring"""





		assert abs_val(0    ) == 0
		assert abs_val(34    ) == 34
		assert abs_val(-100_000_000_000    ) == 100_000_000_000

		a__   		=     [-3, -1, 2, -11]
		assert abs_max(UpperCamelCase    ) == -11
		assert abs_max_sort(UpperCamelCase    ) == -11
		assert abs_min(UpperCamelCase    ) == -1


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					test_abs_val()
					print(abs_val(-34))  # --> 34




