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
851	Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -8 $.	6
852	Find $ a_11 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	6
853	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 3 }{ 4 } ~~ \text{and} ~~ a_{ 3 } = \frac{ 333 }{ 4 } $.	6
854	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = 2 $.	6
855	Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	6
856	Find $ a_5 $ of a geometric progression if $ a_1 = 850 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	6
857	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 0.9 $.	6
858	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	6
859	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	6
860	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	6
861	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	6
862	$$ a_1 = 4 ~,~ r = 4 ~,~ a_n = 4096 ~,~ n = ? $$	6
863	Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	6
864	Find $ a_7 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	6
865	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = -5 $.	6
866	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 0.968 ~~ \text{and} ~~ r = 0.968 $.	6
867	Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 6 $.	6
868	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 150 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	6
869	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	6
870	Find the sum of the first $ 252 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 1.003 $.	6
871	Find $ a_9 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = 3 $.	6
872	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 17 ~~ \text{and} ~~ r = 3 $.	6
873	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = -2 $.	6
874	Find $ a_34 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.128 $.	6
875	Find $ a_39 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.113 $.	6
876	Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	6
877	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	6
878	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	6
879	Find $ a_11 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 81 } ~~ \text{and} ~~ r = 3 $.	6
880	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	6
881	Find $ a_8 $ of a geometric progression if $ a_1 = 3072 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	6
882	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	6
883	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = 1.1 $.	6
884	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	6
885	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 25 ~~ \text{and} ~~ r = 3.08 $.	6
886	Find $ a_2 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = \dfrac{ 77 }{ 25 } $.	6
887	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 25 ~~ \text{and} ~~ a_{ 3 } = 226 $.	6
888	Find $ a_2 $ of a geometric progression if $ a_1 = 226 ~~ \text{and} ~~ r = 3.01 $.	6
889	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	6
890	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 480 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	6
891	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	6
892	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2187 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	6
893	$$ a_1 = 1 ~,~ r = \frac{ 1 }{ 4 } ~,~ S_n = 6 ~,~ n = ? $$	6
894	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 21 }{ 5 } $.	6
895	Find $ a_9 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -3 $.	6
896	Find $ a_7 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 2 $.	6
897	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = -12 ~~ \text{and} ~~ r = -1.5 $.	6
898	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 6 $.	6
899	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	6
900	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	6