Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

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ID	Problem	Count
4851	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
4852	Find $ a_20 $ of a geometric progression if $ a_1 = 640 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4853	Find $ a_20 $ of a geometric progression if $ a_1 = 640 ~~ \text{and} ~~ r = 1.196 $.	2
4854	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 640 ~~ \text{and} ~~ r = 1.191 $.	2
4855	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4856	Find $ a_1 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	2
4857	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 300 ~~ \text{and} ~~ r = 0.1 $.	2
4858	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -4 $.	2
4859	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	2
4860	Find $ a_5 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = \dfrac{ 53 }{ 50 } $.	2
4861	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = \frac{ 53 }{ 50 } $.	2
4862	Find $ a_5 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 1.06 $.	2
4863	Find $ a_60 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 1.06 $.	2
4864	Find $ a_80 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 1.06 $.	2
4865	Find $ a_67 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 1.06 $.	2
4866	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.666 $.	2
4867	Find $ a_20 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
4868	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 8 }{ 5 } $.	2
4869	$$ a_1 = 1 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4870	$$ a_1 = 1 ~,~ r = 2 ~,~ a_n = 1024 ~,~ n = ? $$	2
4871	Find $ a_115 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = -0.5 $.	2
4872	$$ a_1 = -1 ~~,~~ r = -5 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4873	Find $ a_7 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4874	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
4875	Find $ a_4 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = -4 $.	2
4876	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -\frac{ 27 }{ 4 } ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
4877	Find $ a_2500 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 25 } ~~ \text{and} ~~ r = 5 $.	2
4878	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4879	$$ a_1 = 2 ~,~ r = 4 ~,~ a_n = 21 ~,~ n = ? $$	2
4880	Find $ a_15 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4881	Find $ a_8 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4882	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 28000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	2
4883	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 7 } ~~ \text{and} ~~ r = 7 $.	2
4884	Find $ a_9 $ of a geometric progression if $ a_1 = 13122 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4885	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 25 }{ 16 } ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	2
4886	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 103 }{ 100 } $.	2
4887	Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -2 $.	2
4888	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	2
4889	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	2
4890	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4891	Find $ a_16 $ of a geometric progression if $ a_1 = 177147 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4892	Find $ a_16 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
4893	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 10 $.	2
4894	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -72 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
4895	Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = 0.9346 $.	2
4896	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	2
4897	Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4898	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	2
4899	Find $ a_4 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	2
4900	Find $ a_59 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = 1.1 $.	2