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
5051	Find $ a_22 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $.	2
5052	Find $ a_8 $ of a geometric progression if $ a_1 = 896 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5053	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 1 $.	2
5054	Find $ a_3 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	2
5055	Find $ a_10 $ of a geometric progression if $ a_1 = 0.66 ~~ \text{and} ~~ r = 0.75 $.	2
5056	Find $ a_50 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
5057	$$ a_1 = 230 ~~,~~ r = \frac{ 1 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
5058	Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 5 $.	2
5059	Find $ a_5 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
5060	Find $ a_5 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = 2 $.	2
5061	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.00012 ~~ \text{and} ~~ r = 1.25 $.	2
5062	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 0.0001 ~~ \text{and} ~~ r = 1.24 $.	2
5063	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 0.0001 ~~ \text{and} ~~ r = 1.22 $.	2
5064	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 0.0001 ~~ \text{and} ~~ r = 1.2 $.	2
5065	Find the sum of the first $ 60 $ terms of a geometric sequence if $ a_1 = 0.0001 ~~ \text{and} ~~ r = 1.2 $.	2
5066	Find $ a_1 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 50 } $.	2
5067	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 16807 ~~ \text{and} ~~ r = -\frac{ 1 }{ 7 } $.	2
5068	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 0.00012 ~~ \text{and} ~~ r = 1.25 $.	2
5069	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 0.0001 ~~ \text{and} ~~ r = 1.24 $.	2
5070	Find the sum of the first $ 70 $ terms of a geometric sequence if $ a_1 = 0.0001 ~~ \text{and} ~~ r = 1.14 $.	2
5071	Find $ a_4 $ of a geometric progression if $ a_1 = 48 ~~ \text{and} ~~ r = -4 $.	2
5072	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 144 ~~ \text{and} ~~ a_{ 8 } = 1152 $.	2
5073	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 9 } = 64 ~~ \text{and} ~~ a_{ 14 } = 99 $.	2
5074	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 32 ~~ \text{and} ~~ a_{ 8 } = 256 $.	2
5075	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 128 ~~ \text{and} ~~ a_{ 9 } = 2048 $.	2
5076	Find $ a_5 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	2
5077	Find $ a_10 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = -9 $.	2
5078	Find $ a_10 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 12 $.	2
5079	Find $ a_4 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 5 $.	2
5080	Find $ a_5 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
5081	Find $ a_2 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5082	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 19 }{ 10 } ~~ \text{and} ~~ r = -3 $.	2
5083	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 17 }{ 10 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
5084	Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 5 } $.	2
5085	Find $ a_4 $ of a geometric progression if $ a_1 = -13 ~~ \text{and} ~~ r = -4 $.	2
5086	Find $ a_4 $ of a geometric progression if $ a_1 = -219 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
5087	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 42 ~~ \text{and} ~~ a_{ 5 } = \frac{ 567 }{ 4 } $.	2
5088	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
5089	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
5090	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2
5091	$$ a_1 = \frac{ 109 }{ 50 } ~,~ r = \frac{ 61 }{ 50 } ~,~ S_n = \frac{ 157 }{ 2 } ~,~ n = ? $$	2
5092	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -15 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2
5093	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -20 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2
5094	$$ a_1 = 10 ~,~ r = 0.22 ~,~ S_n = 360 ~,~ n = ? $$	2
5095	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 10 $.	2
5096	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 3 ~~ \text{and} ~~ a_{ 2 } = \frac{ 9 }{ 5 } $.	2
5097	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	2
5098	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	2
5099	Find $ a_14 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	2
5100	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 30000 ~~ \text{and} ~~ r = 1.09 $.	2