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
10951	Find $ a_7 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	1
10952	Find $ a_17 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 3 $.	1
10953	Find $ a_17 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	1
10954	Find $ a_6 $ of a geometric progression if $ a_1 = -14 ~~ \text{and} ~~ r = 2 $.	1
10955	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	1
10956	Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 8 $.	1
10957	Find $ a_10 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10958	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 405 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
10959	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 405 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
10960	Find $ a_15 $ of a geometric progression if $ a_1 = 405 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10961	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 405 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
10962	Find $ a_15 $ of a geometric progression if $ a_1 = 405 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
10963	Find $ a_15 $ of a geometric progression if $ a_1 = 405 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
10964	Find $ a_15 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 2 $.	1
10965	Find $ a_5 $ of a geometric progression if $ a_1 = 28 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10966	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 1 ~~ \text{and} ~~ a_{ 5 } = 27 $.	1
10967	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 1 ~~ \text{and} ~~ a_{ 4 } = 3 $.	1
10968	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.442 $.	1
10969	Find $ a_5 $ of a geometric progression if $ a_1 = -27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
10970	Find $ a_17 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	1
10971	Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -1 $.	1
10972	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2401 } ~~ \text{and} ~~ r = 1 $.	1
10973	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	1
10974	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	1
10975	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	1
10976	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	1
10977	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	1
10978	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	1
10979	Find $ a_6 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.5 $.	1
10980	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	1
10981	Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 7 $.	1
10982	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 4 ~~ \text{and} ~~ a_{ 6 } = 27 $.	1
10983	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 88 ~~ \text{and} ~~ r = 2 $.	1
10984	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 88 ~~ \text{and} ~~ r = 2 $.	1
10985	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 80 ~~ \text{and} ~~ r = 2 $.	1
10986	Find $ a_14 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	1
10987	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0.0768 ~~ \text{and} ~~ r = 2 $.	1
10988	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0.007813 ~~ \text{and} ~~ r = 2 $.	1
10989	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 43 ~~ \text{and} ~~ r = 2 $.	1
10990	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 625 }{ 4 } ~~ \text{and} ~~ r = 2 $.	1
10991	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = \frac{ 81 }{ 64 } ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
10992	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 50 } ~~ \text{and} ~~ r = 2 $.	1
10993	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 0.023 ~~ \text{and} ~~ r = 2 $.	1
10994	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 21 ~~ \text{and} ~~ r = 2 $.	1
10995	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = 2 $.	1
10996	Find $ a_16 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	1
10997	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
10998	Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
10999	$$ a_1 = 1500000 ~,~ r = \frac{ 1 }{ 10 } ~,~ a_n = 5 ~,~ n = ? $$	1
11000	Find $ a_6 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.	1