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
10901	Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 8 $.	1
10902	Find $ a_4 $ of a geometric progression if $ a_1 = -32 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $.	1
10903	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 703 }{ 100 } ~~ \text{and} ~~ r = -5 $.	1
10904	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
10905	Find $ a_4 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 3 $.	1
10906	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 9 $.	1
10907	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 9 $.	1
10908	$$ a_1 = 100 ~,~ r = 2 ~,~ a_n = 5 ~,~ n = ? $$	1
10909	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 25 } $.	1
10910	Find $ a_5 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.03 $.	1
10911	Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10912	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = -\frac{ 5 }{ 4 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	1
10913	Find the sum of the first $ 900000000 $ terms of a geometric sequence if $ a_1 = -0.9614 ~~ \text{and} ~~ r = -0.9614 $.	1
10914	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -20 ~~ \text{and} ~~ r = 3 $.	1
10915	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
10916	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
10917	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
10918	Find $ a_10 $ of a geometric progression if $ a_1 = 237000 ~~ \text{and} ~~ r = 0.865 $.	1
10919	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2400 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
10920	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
10921	Find $ a_10 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 3 $.	1
10922	Find $ a_11 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 3 $.	1
10923	Find $ a_6 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
10924	Find $ a_5 $ of a geometric progression if $ a_1 = 155000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	1
10925	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 200000 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
10926	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
10927	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
10928	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 12 ~~ \text{and} ~~ a_{ 5 } = 96 $.	1
10929	Find $ a_18 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -3 $.	1
10930	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 2048 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10931	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 16384 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10932	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 16384 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10933	Find $ a_8 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 6 $.	1
10934	$$ a_1 = 2 ~,~ r = \frac{ 1 }{ 4 } ~,~ a_n = \frac{ 1 }{ 2048 } ~,~ n = ? $$	1
10935	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 9 } ~~ \text{and} ~~ r = -3 $.	1
10936	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	1
10937	Find $ a_21 $ of a geometric progression if $ a_1 = 16387 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10938	Find $ a_3 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	1
10939	Find $ a_13 $ of a geometric progression if $ a_1 = 24576 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10940	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $.	1
10941	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 10 $.	1
10942	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	1
10943	$$ a_1 = 50 ~,~ r = 1.99 ~,~ a_n = 50 ~,~ n = ? $$	1
10944	Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10945	Find $ a_18 $ of a geometric progression if $ a_1 = -25 ~~ \text{and} ~~ r = 4 $.	1
10946	Find $ a_18 $ of a geometric progression if $ a_1 = -25 ~~ \text{and} ~~ r = 3 $.	1
10947	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 9 }{ 10 } ~~ \text{and} ~~ r = 1 $.	1
10948	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
10949	Find the sum of the first $ 9999999999 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
10950	Find $ a_6 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1