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
901	Find $ a_9 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = 2 $.	6
902	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	6
903	Find $ a_10 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	6
904	Find $ a_6 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	6
905	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	6
906	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	6
907	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.	6
908	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 0.01 ~~ \text{and} ~~ r = 2 $.	6
909	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	6
910	$$ a_1 = 1 ~~,~~ r = 3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	6
911	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	6
912	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	6
913	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	6
914	Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	6
915	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	6
916	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = 4 $.	6
917	$$ a_1 = 3 ~,~ r = 2 ~,~ a_n = 5 ~,~ n = ? $$	6
918	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 2 }{ 3 } ~~ \text{and} ~~ a_{ 3 } = 171 $.	6
919	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 65536 ~~ \text{and} ~~ a_{ 6 } = 8192 $.	6
920	Find $ a_4 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 2 $.	6
921	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 3 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	6
922	Find $ a_100 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	6
923	Find $ a_3 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 20 } $.	6
924	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	6
925	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	6
926	Find the sum of the first $ 1000000 $ terms of a geometric sequence if $ a_1 = 96 ~~ \text{and} ~~ r = 0.5 $.	6
927	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -12 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	6
928	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	6
929	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	6
930	Find $ a_12 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	6
931	Find $ a_9 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -4 $.	6
932	Find $ a_31 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	6
933	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	6
934	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 8 $.	6
935	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	6
936	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 50 ~~ \text{and} ~~ a_{ 4 } = \frac{ 225 }{ 2 } $.	6
937	Find $ a_8 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 2 $.	6
938	Find $ a_8 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	6
939	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	6
940	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	6
941	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	6
942	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 8 ~~ \text{and} ~~ a_{ 8 } = 64 $.	6
943	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 18 ~~ \text{and} ~~ a_{ 5 } = \frac{ 9 }{ 2 } $.	6
944	Find $ a_5 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $.	6
945	Find $ a_4 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $.	6
946	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	6
947	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	6
948	Find $ a_5 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	6
949	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 9 $.	6
950	Find $ a_5 $ of a geometric progression if $ a_1 = 162 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	6