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
4151	Find $ a_5 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = 1 $.	2
4152	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
4153	Find $ a_13 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4154	Find $ a_6 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4155	$$ a_1 = 2 ~,~ r = 3 ~,~ a_n = 12 ~,~ n = ? $$	2
4156	Find the sum of the first $ 75 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 3 } ~~ \text{and} ~~ r = 3 $.	2
4157	Find the sum of the first $ 76 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 3 } ~~ \text{and} ~~ r = -3 $.	2
4158	Find $ a_5 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4159	Find $ a_11 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4160	Find $ a_2 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 5 $.	2
4161	Find $ a_2 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 0.2 $.	2
4162	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4163	Find $ a_12 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	2
4164	Find $ a_1 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 3 $.	2
4165	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0.0035 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
4166	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = -2 $.	2
4167	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4168	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4169	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 0.5 ~~ \text{and} ~~ r = 2 $.	2
4170	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 5 $.	2
4171	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4000 ~~ \text{and} ~~ r = \frac{ 8 }{ 5 } $.	2
4172	Find $ a_10 $ of a geometric progression if $ a_1 = 60000 ~~ \text{and} ~~ r = 1 $.	2
4173	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ a_{ 5 } = \frac{ 1 }{ 32 } $.	2
4174	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1200 ~~ \text{and} ~~ r = 0.003 $.	2
4175	Find $ a_10 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = 2 $.	2
4176	Find $ a_9 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = 2 $.	2
4177	Find $ a_6 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = 2 $.	2
4178	Find $ a_9 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 6 $.	2
4179	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 4 } ~~ \text{and} ~~ r = -\dfrac{ 6 }{ 5 } $.	2
4180	Find $ a_6 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	2
4181	Find $ a_5 $ of a geometric progression if $ a_1 = 22 ~~ \text{and} ~~ r = 4 $.	2
4182	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -4 $.	2
4183	Find $ a_8 $ of a geometric progression if $ a_1 = 648 ~~ \text{and} ~~ r = \dfrac{ 37 }{ 12 } $.	2
4184	Find $ a_8 $ of a geometric progression if $ a_1 = 648 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4185	Find $ a_6 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 5 $.	2
4186	Find $ a_100 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.02 $.	2
4187	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 10 } = 25 ~~ \text{and} ~~ a_{ 12 } = 225 $.	2
4188	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 20 ~~ \text{and} ~~ a_{ 5 } = 1280 $.	2
4189	Find the sum of the first $ 100000000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
4190	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4191	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4192	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 4.09 ~~ \text{and} ~~ r = 1.07 $.	2
4193	Find $ a_15 $ of a geometric progression if $ a_1 = 4.09 ~~ \text{and} ~~ r = 1.07 $.	2
4194	Find $ a_10 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	2
4195	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4196	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	2
4197	Find $ a_1 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 4 } $.	2
4198	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 4 } $.	2
4199	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	2
4200	Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 4 } $.	2