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
8001	Find $ a_25 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8002	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
8003	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $.	1
8004	Find $ a_30 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
8005	Find $ a_14 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	1
8006	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	1
8007	Find $ a_11 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	1
8008	Find $ a_3 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
8009	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
8010	Find $ a_5 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 5 $.	1
8011	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0.403 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
8012	Find $ a_365 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.01 $.	1
8013	Find $ a_365 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.02 $.	1
8014	Find $ a_100 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 1.02 $.	1
8015	Find $ a_20 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.02 $.	1
8016	Find $ a_30 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.02 $.	1
8017	Find $ a_30 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 1.02 $.	1
8018	Find $ a_15 $ of a geometric progression if $ a_1 = 135 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
8019	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 20 ~~ \text{and} ~~ a_{ 5 } = 2500 $.	1
8020	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 1 }{ 5 } $.	1
8021	Find $ a_1 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 6 $.	1
8022	Find $ a_12 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.135 $.	1
8023	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
8024	Find $ a_4 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8025	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
8026	Find $ a_10 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = -0.75 $.	1
8027	Find $ a_5 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
8028	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 5 ~~ \text{and} ~~ a_{ 6 } = 15 $.	1
8029	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
8030	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
8031	Find $ a_11 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -7 $.	1
8032	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 60000 ~~ \text{and} ~~ r = \frac{ 23 }{ 20 } $.	1
8033	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 26 }{ 27 } $.	1
8034	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 500 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
8035	Find $ a_10 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
8036	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
8037	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
8038	Find the sum of the first $ 480 $ terms of a geometric sequence if $ a_1 = 500 ~~ \text{and} ~~ r = 1.006 $.	1
8039	Find the sum of the first $ 480 $ terms of a geometric sequence if $ a_1 = 500 ~~ \text{and} ~~ r = 1.006 $.	1
8040	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 343 } ~~ \text{and} ~~ r = 7 $.	1
8041	Find $ a_2 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	1
8042	Find $ a_10 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	1
8043	$$ a_1 = 6 ~,~ r = 2 ~,~ a_n = 8 ~,~ n = ? $$	1
8044	Find $ a_60 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.005 $.	1
8045	Find $ a_2 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 25 $.	1
8046	Find the sum of the first $ 360 $ terms of a geometric sequence if $ a_1 = 51 ~~ \text{and} ~~ r = 1.02 $.	1
8047	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 1 $.	1
8048	$$ a_1 = 1133 ~,~ r = 0.00967 ~,~ S_n = 37890 ~,~ n = ? $$	1
8049	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1500 ~~ \text{and} ~~ r = 2 $.	1
8050	Find $ a_2 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 2 $.	1