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
8801	Find $ a_3 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
8802	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 6 }{ 5 } $.	1
8803	Find $ a_18 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	1
8804	Find $ a_10 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $.	1
8805	Find $ a_16 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 0.04 $.	1
8806	Find $ a_16 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = -0.04 $.	1
8807	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 81 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
8808	Find $ a_1 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 10 $.	1
8809	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
8810	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 0.5 $.	1
8811	Find $ a_9 $ of a geometric progression if $ a_1 = 176534 ~~ \text{and} ~~ r = 0.074 $.	1
8812	Find $ a_29 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -2 $.	1
8813	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 7 }{ 4 } $.	1
8814	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 7 }{ 4 } $.	1
8815	Find $ a_11 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.	1
8816	Find $ a_9 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = -3 $.	1
8817	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = -3 $.	1
8818	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 6 } = 729 ~~ \text{and} ~~ a_{ 2 } = \frac{ 1 }{ 9 } $.	1
8819	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 62 ~~ \text{and} ~~ a_{ 5 } = 496 $.	1
8820	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -1.414 $.	1
8821	Find $ a_12 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -3 $.	1
8822	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
8823	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
8824	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ r = 2 $.	1
8825	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 8 $.	1
8826	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 8 $.	1
8827	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 6 $.	1
8828	Find $ a_10 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	1
8829	Find $ a_9 $ of a geometric progression if $ a_1 = 3000000 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
8830	Find $ a_3 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -6 $.	1
8831	Find $ a_11 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 6 $.	1
8832	$$ a_1 = 400 ~,~ r = \frac{ 3 }{ 2 } ~,~ a_n = 7 ~,~ n = ? $$	1
8833	Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -1 $.	1
8834	Find $ a_9 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8835	Find $ a_6 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	1
8836	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = -3 $.	1
8837	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 2 }{ 7 } $.	1
8838	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 10 $.	1
8839	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 34 }{ 3 } ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
8840	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 34 }{ 3 } ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
8841	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	1
8842	Find $ a_8 $ of a geometric progression if $ a_1 = 243 ~~ \text{and} ~~ r = 3 $.	1
8843	Find $ a_9 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 2 $.	1
8844	Find $ a_11 $ of a geometric progression if $ a_1 = 1000000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	1
8845	Find $ a_2 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 17 }{ 20 } $.	1
8846	Find $ a_2 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	1
8847	Find $ a_6 $ of a geometric progression if $ a_1 = 896 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8848	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 896 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
8849	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 3 $.	1
8850	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 243 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1