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
4051	Find $ a_3 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 16 $.	2
4052	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4053	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
4054	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 14 ~~ \text{and} ~~ a_{ 5 } = 112 $.	2
4055	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	2
4056	Find $ a_5 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = -4 $.	2
4057	Find $ a_15 $ of a geometric progression if $ a_1 = 7.071 ~~ \text{and} ~~ r = 1.414 $.	2
4058	Find $ a_4 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.	2
4059	Find $ a_22 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = 1.025 $.	2
4060	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 240 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
4061	Find $ a_6 $ of a geometric progression if $ a_1 = 376 ~~ \text{and} ~~ r = 2 $.	2
4062	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 1536 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4063	Find $ a_7 $ of a geometric progression if $ a_1 = -\dfrac{ 1536 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4064	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 1536 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4065	Find $ a_10 $ of a geometric progression if $ a_1 = -\dfrac{ 1536 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4066	Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	2
4067	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = 0.96 $.	2
4068	Find $ a_40 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	2
4069	Find $ a_40 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 10 $.	2
4070	Find $ a_15 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $.	2
4071	Find $ a_7 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.	2
4072	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 0.1 ~~ \text{and} ~~ r = 1.5 $.	2
4073	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 4 $.	2
4074	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 4 $.	2
4075	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = 4 $.	2
4076	Find $ a_4 $ of a geometric progression if $ a_1 = -2.5 ~~ \text{and} ~~ r = 1.5 $.	2
4077	Find $ a_4 $ of a geometric progression if $ a_1 = -2.5 ~~ \text{and} ~~ r = -1.5 $.	2
4078	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $.	2
4079	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 2400 ~~ \text{and} ~~ r = 0.011 $.	2
4080	Find $ a_12 $ of a geometric progression if $ a_1 = 2400 ~~ \text{and} ~~ r = 1.011 $.	2
4081	Find $ a_24 $ of a geometric progression if $ a_1 = 2400 ~~ \text{and} ~~ r = 1.011 $.	2
4082	Find $ a_60 $ of a geometric progression if $ a_1 = 2400 ~~ \text{and} ~~ r = 1.011 $.	2
4083	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	2
4084	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
4085	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 6 } = 750 ~~ \text{and} ~~ a_{ 10 } = 3200 $.	2
4086	Find $ a_14 $ of a geometric progression if $ a_1 = 122.3 ~~ \text{and} ~~ r = 1.437 $.	2
4087	Find the sum of the first $ 26 $ terms of a geometric sequence if $ a_1 = 0.005 ~~ \text{and} ~~ r = 1.2 $.	2
4088	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 1 ~~ \text{and} ~~ a_{ 5 } = 64 $.	2
4089	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 27 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.	2
4090	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 5 } $.	2
4091	Find $ a_2 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 1 $.	2
4092	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 2700 ~~ \text{and} ~~ a_{ 2 } = 2430 $.	2
4093	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7000 ~~ \text{and} ~~ r = 0.013 $.	2
4094	Find $ a_12 $ of a geometric progression if $ a_1 = 7000 ~~ \text{and} ~~ r = 0.013 $.	2
4095	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7000 ~~ \text{and} ~~ r = 1.013 $.	2
4096	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 8 }{ 3 } ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
4097	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 66000 ~~ \text{and} ~~ r = 0.957 $.	2
4098	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 66000 ~~ \text{and} ~~ r = 0.957 $.	2
4099	Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 5 $.	2
4100	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 400 ~~ \text{and} ~~ r = 1.075 $.	2