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
6151	Find $ a_6 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	2
6152	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 63 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
6153	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 5 }{ 6 } $.	2
6154	Find $ a_2 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6155	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6156	Find $ a_19 $ of a geometric progression if $ a_1 = 221 ~~ \text{and} ~~ r = 1.06 $.	2
6157	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 1.2 $.	2
6158	Find $ a_5 $ of a geometric progression if $ a_1 = 2423 ~~ \text{and} ~~ r = 4 $.	2
6159	Find $ a_1 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
6160	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 7 }{ 10 } $.	2
6161	Find $ a_5 $ of a geometric progression if $ a_1 = 48 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
6162	Find $ a_5 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
6163	Find $ a_6 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
6164	Find $ a_5 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
6165	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 35 ~~ \text{and} ~~ a_{ 5 } = \frac{ 625 }{ 4 } $.	2
6166	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 25 ~~ \text{and} ~~ a_{ 5 } = \frac{ 625 }{ 4 } $.	2
6167	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 75 ~~ \text{and} ~~ r = 1.02 $.	2
6168	Find $ a_2 $ of a geometric progression if $ a_1 = -\dfrac{ 5 }{ 4 } ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 7 } $.	2
6169	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.	2
6170	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 800 ~~ \text{and} ~~ r = 1.05 $.	2
6171	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 6 } ~~ \text{and} ~~ r = \frac{ 125 }{ 216 } $.	2
6172	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.5 $.	2
6173	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = \frac{ 93 }{ 100 } ~~ \text{and} ~~ r = 0.025 $.	2
6174	Find $ a_1000 $ of a geometric progression if $ a_1 = \dfrac{ 93 }{ 100 } ~~ \text{and} ~~ r = 1.023 $.	2
6175	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
6176	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $.	2
6177	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	2
6178	Find $ a_10 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 2 $.	2
6179	Find $ a_12 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	2
6180	Find $ a_7 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.	2
6181	Find $ a_8 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.	2
6182	Find $ a_10 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.	2
6183	Find $ a_12 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.	2
6184	Find $ a_5 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 2 $.	2
6185	Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = 1.1 $.	2
6186	Find $ a_100 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	2
6187	Find $ a_12 $ of a geometric progression if $ a_1 = 83 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 7 } $.	2
6188	$$ a_1 = 6 ~,~ r = \frac{ 2 }{ 3 } ~,~ a_n = 10 ~,~ n = ? $$	2
6189	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 16.21 ~~ \text{and} ~~ r = 0.9345 $.	2
6190	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 3.481 ~~ \text{and} ~~ r = 0.9434 $.	2
6191	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0.0987 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2
6192	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0.09877 ~~ \text{and} ~~ r = 0.1975 $.	2
6193	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 6 $.	2
6194	Find the sum of the first $ 999999 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2
6195	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2
6196	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
6197	Find $ a_6 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
6198	Find $ a_1 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	2
6199	Find $ a_1 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $.	2
6200	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 16 }{ 15 } $.	2