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
5901	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 2 } ~~ \text{and} ~~ r = 2 $.	2
5902	Find $ a_5 $ of a geometric progression if $ a_1 = 15000 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	2
5903	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 75 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5904	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 75 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5905	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 10 ~~ \text{and} ~~ a_{ 6 } = 80 $.	2
5906	Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5907	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5908	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5909	Find $ a_5 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5910	Find $ a_6 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5911	Find $ a_5 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -4 $.	2
5912	Find $ a_6 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -4 $.	2
5913	Find $ a_7 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -4 $.	2
5914	Find $ a_5 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
5915	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 0.75 $.	2
5916	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = \frac{ 141 }{ 100 } $.	2
5917	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 2100 ~~ \text{and} ~~ r = 1.012 $.	2
5918	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 64341 }{ 100 } ~~ \text{and} ~~ r = 0.036 $.	2
5919	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	2
5920	Find $ a_3 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5921	Find $ a_5 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = 2 $.	2
5922	Find $ a_4 $ of a geometric progression if $ a_1 = 160 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	2
5923	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
5924	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	2
5925	Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
5926	Find $ a_7 $ of a geometric progression if $ a_1 = 50500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
5927	Find $ a_10 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -3 $.	2
5928	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -7 $.	2
5929	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
5930	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
5931	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
5932	Find the sum of the first $ 23 $ terms of a geometric sequence if $ a_1 = 160000 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
5933	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5934	Find $ a_1 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = 2 $.	2
5935	Find $ a_2 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -8 $.	2
5936	Find $ a_3 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -8 $.	2
5937	Find $ a_2 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5938	Find $ a_7 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 12 $.	2
5939	Find $ a_13 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	2
5940	Find $ a_11 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.	2
5941	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 0.0048 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2
5942	Find $ a_16 $ of a geometric progression if $ a_1 = 2.5 ~~ \text{and} ~~ r = 6 $.	2
5943	Find $ a_13 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 5 $.	2
5944	Find the sum of the first $ 365 $ terms of a geometric sequence if $ a_1 = 0.25 ~~ \text{and} ~~ r = 2 $.	2
5945	Find $ a_6 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -4 $.	2
5946	Find $ a_7 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 2 $.	2
5947	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $.	2
5948	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 100 } ~~ \text{and} ~~ r = 10 $.	2
5949	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 48000 ~~ \text{and} ~~ r = 1.05 $.	2
5950	Find $ a_360 $ of a geometric progression if $ a_1 = \dfrac{ 3991 }{ 4 } ~~ \text{and} ~~ r = 0.0035 $.	2