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
9001	Find $ a_5 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9002	Find $ a_2 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
9003	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 729 } ~~ \text{and} ~~ r = 3 $.	1
9004	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 40 ~~ \text{and} ~~ a_{ 10 } = \frac{ 1215 }{ 4 } $.	1
9005	Find first element ( $ a_1 $ ) of a geometic progression if $ r = -\frac{ 4 }{ 5 } ~~ \text{and} ~~ a_{ 6 } = -1280 $.	1
9006	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	1
9007	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = 4 $.	1
9008	Find $ a_9 $ of a geometric progression if $ a_1 = 384 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	1
9009	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 6 ~~ \text{and} ~~ a_{ 20 } = 324 $.	1
9010	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 6 ~~ \text{and} ~~ a_{ 20 } = 324 $.	1
9011	$$ a_1 = \frac{ 37 }{ 1048576 } ~,~ r = 4 ~,~ a_n = 12 ~,~ n = ? $$	1
9012	Find the sum of the first $ 38 $ terms of a geometric sequence if $ a_1 = 355 ~~ \text{and} ~~ r = 348 $.	1
9013	Find $ a_38 $ of a geometric progression if $ a_1 = 355 ~~ \text{and} ~~ r = 0.981 $.	1
9014	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
9015	Find $ a_12 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = -2 $.	1
9016	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 700 ~~ \text{and} ~~ r = 1.066 $.	1
9017	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 700 ~~ \text{and} ~~ r = 1.082 $.	1
9018	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 700 ~~ \text{and} ~~ r = 1.13 $.	1
9019	Find $ a_15 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
9020	Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
9021	Find $ a_1 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
9022	Find $ a_3 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
9023	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 125 $.	1
9024	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 25 $.	1
9025	Find $ a_3 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -6 $.	1
9026	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 16 $.	1
9027	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 12 $.	1
9028	Find $ a_3 $ of a geometric progression if $ a_1 = 2.3 ~~ \text{and} ~~ r = 0.24 $.	1
9029	Find $ a_3 $ of a geometric progression if $ a_1 = 2.3 ~~ \text{and} ~~ r = 0.22 $.	1
9030	Find $ a_3 $ of a geometric progression if $ a_1 = 2.3 ~~ \text{and} ~~ r = 0.69 $.	1
9031	Find $ a_11 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $.	1
9032	Find $ a_9 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	1
9033	Find the sum of the first $ 77 $ terms of a geometric sequence if $ a_1 = 661.5 ~~ \text{and} ~~ r = 1.05 $.	1
9034	Find $ a_50 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9035	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	1
9036	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 4 $.	1
9037	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 4 $.	1
9038	Find $ a_16 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 8 $.	1
9039	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
9040	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	1
9041	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	1
9042	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	1
9043	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	1
9044	Find $ a_2 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
9045	$$ a_1 = 15 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	1
9046	Find $ a_6 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 2 $.	1
9047	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
9048	Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 0.1429 $.	1
9049	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -2 $.	1
9050	Find $ a_100 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	1