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
4801	Find $ a_5 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4802	Find the sum of the first $ 18750 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 5 $.	2
4803	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 5 $.	2
4804	Find $ a_6 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -3 $.	2
4805	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $.	2
4806	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -6 $.	2
4807	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -6 $.	2
4808	Find $ a_6 $ of a geometric progression if $ a_1 = 120 ~~ \text{and} ~~ r = 2 $.	2
4809	Find $ a_100 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4810	Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 5 $.	2
4811	$$ a_1 = 2 ~,~ r = \frac{ 1 }{ 4 } ~,~ a_n = 15 ~,~ n = ? $$	2
4812	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4813	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $.	2
4814	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	2
4815	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ r = 2 $.	2
4816	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -\frac{ 8 }{ 3 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
4817	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
4818	Find $ a_6 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
4819	Find $ a_5 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	2
4820	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -3 $.	2
4821	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 75 ~~ \text{and} ~~ r = 0.8 $.	2
4822	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = -3 $.	2
4823	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0.671 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
4824	Find $ a_4 $ of a geometric progression if $ a_1 = 21000 ~~ \text{and} ~~ r = 3 $.	2
4825	Find $ a_4 $ of a geometric progression if $ a_1 = 21000 ~~ \text{and} ~~ r = \dfrac{ 103 }{ 100 } $.	2
4826	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.367 $.	2
4827	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.248 $.	2
4828	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.479 $.	2
4829	Find $ a_4 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
4830	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -0.5 $.	2
4831	Find $ a_5 $ of a geometric progression if $ a_1 = 125 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
4832	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 12 ~~ \text{and} ~~ a_{ 4 } = 5 $.	2
4833	Find $ a_9 $ of a geometric progression if $ a_1 = 500000 ~~ \text{and} ~~ r = 0.99 $.	2
4834	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = -\frac{ 5 }{ 2 } $.	2
4835	Find $ a_9 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4836	$$ a_1 = 10 ~,~ r = \frac{ 61 }{ 50 } ~,~ a_n = 2 ~,~ n = ? $$	2
4837	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.	2
4838	Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 6 $.	2
4839	Find $ a_8 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = -2 $.	2
4840	Find $ a_8 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = -2 $.	2
4841	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = -4 $.	2
4842	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = -4 $.	2
4843	Find $ a_10 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4844	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
4845	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.87 $.	2
4846	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = -0.87 $.	2
4847	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -3 $.	2
4848	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
4849	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	2
4850	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	2