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
6051	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
6052	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
6053	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6054	Find $ a_5 $ of a geometric progression if $ a_1 = 7000000 ~~ \text{and} ~~ r = \dfrac{ 97 }{ 100 } $.	2
6055	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -\frac{ 3 }{ 4 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
6056	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
6057	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
6058	$$ a_1 = 84 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
6059	Find $ a_3 $ of a geometric progression if $ a_1 = 22000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 20 } $.	2
6060	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2
6061	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = \frac{ 1 }{ 6 } ~~ \text{and} ~~ a_{ 3 } = \frac{ 1 }{ 9 } $.	2
6062	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 2 } $.	2
6063	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 4 } $.	2
6064	$$ a_1 = 4 ~~,~~ r = -3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
6065	Find $ a_5 $ of a geometric progression if $ a_1 = 1875 ~~ \text{and} ~~ r = 0.2 $.	2
6066	Find $ a_2 $ of a geometric progression if $ a_1 = 1875 ~~ \text{and} ~~ r = 0.2 $.	2
6067	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6068	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 35 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	2
6069	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 9 }{ 8 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 1 }{ 4 } $.	2
6070	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 8 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	2
6071	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
6072	Find the sum of the first $ 9223372036854775807 $ terms of a geometric sequence if $ a_1 = 80010 ~~ \text{and} ~~ r = 10.07 $.	2
6073	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -16 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
6074	Find $ a_8 $ of a geometric progression if $ a_1 = 44000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
6075	Find $ a_8 $ of a geometric progression if $ a_1 = 44000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
6076	Find first element ( $ a_1 $ ) of a geometic progression if $ r = -4 ~~ \text{and} ~~ a_{ 12 } = -37 $.	2
6077	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 19 ~~ \text{and} ~~ r = 6 $.	2
6078	Find the sum of the first $ 24 $ terms of a geometric sequence if $ a_1 = 500 ~~ \text{and} ~~ r = 2 $.	2
6079	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0.0077 ~~ \text{and} ~~ r = 775 $.	2
6080	Find the sum of the first $ 1188 $ terms of a geometric sequence if $ a_1 = 33 ~~ \text{and} ~~ r = 1155 $.	2
6081	Find the sum of the first $ 32 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = 1.15 $.	2
6082	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 80 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
6083	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 80 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
6084	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -\frac{ 3 }{ 7 } ~~ \text{and} ~~ r = -\frac{ 3 }{ 7 } $.	2
6085	Find $ a_4 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = 3 $.	2
6086	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 27 }{ 125 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
6087	Find $ a_5 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
6088	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 320 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
6089	$$ a_1 = 320 ~,~ r = \frac{ 1 }{ 4 } ~,~ a_n = 9 ~,~ n = ? $$	2
6090	Find $ a_10 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
6091	Find the sum of the first $ 240 $ terms of a geometric sequence if $ a_1 = \frac{ 2763 }{ 2 } ~~ \text{and} ~~ r = 1 $.	2
6092	Find $ a_7 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6093	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 4 ~~ \text{and} ~~ a_{ 4 } = 256 $.	2
6094	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
6095	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6096	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.1 $.	2
6097	Find $ a_6 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6098	Find $ a_1000000 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 6 } $.	2
6099	Find $ a_2 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 7 $.	2
6100	$$ a_1 = 5 ~,~ r = 5 ~,~ a_n = 5 ~,~ n = ? $$	2