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
801	Find $ a_12 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	6
802	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	6
803	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = 3 $.	6
804	Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 4 $.	6
805	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	6
806	Find $ a_9 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	6
807	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = \frac{ 2 }{ 3 } ~~ \text{and} ~~ a_{ 4 } = \frac{ 3 }{ 4 } $.	6
808	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $.	6
809	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -5 $.	6
810	Find $ a_13 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	6
811	Find $ a_11 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	6
812	Find $ a_2 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 6 $.	6
813	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	6
814	$$ a_1 = 5 ~,~ r = 3 ~,~ a_n = 135 ~,~ n = ? $$	6
815	Find $ a_7 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	6
816	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	6
817	Find $ a_7 $ of a geometric progression if $ a_1 = 729 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	6
818	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	6
819	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -3 $.	6
820	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	6
821	Find $ a_20 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $.	6
822	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $.	6
823	Find $ a_9 $ of a geometric progression if $ a_1 = -65536 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	6
824	Find $ a_6 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $.	6
825	Find $ a_13 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	6
826	Find $ a_1 $ of a geometric progression if $ a_1 = 3125 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	6
827	Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	6
828	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	6
829	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 1.22 $.	6
830	Find $ a_8 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $.	6
831	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	6
832	Find $ a_13 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $.	6
833	Find $ a_12 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	6
834	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	6
835	Find $ a_6 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	6
836	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ r = 2 $.	6
837	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 8 $.	6
838	Find $ a_11 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $.	6
839	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 4 $.	6
840	Find $ a_8 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	6
841	Find $ a_8 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	6
842	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	6
843	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	6
844	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	6
845	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	6
846	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 26 ~~ \text{and} ~~ r = -5 $.	6
847	Find $ a_11 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	6
848	Find $ a_20 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	6
849	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 2 $.	6
850	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 200000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	6