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
4101	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0.75 ~~ \text{and} ~~ r = 5 $.	2
4102	Find $ a_11 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
4103	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.	2
4104	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 22 } ~~ \text{and} ~~ r = 2 $.	2
4105	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
4106	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
4107	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4108	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
4109	Find $ a_8 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4110	Find $ a_10 $ of a geometric progression if $ a_1 = -0.125 ~~ \text{and} ~~ r = -2 $.	2
4111	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	2
4112	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 12 } ~~ \text{and} ~~ r = \dfrac{ 49 }{ 9 } $.	2
4113	Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	2
4114	Find $ a_6 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = 77 $.	2
4115	Find $ a_6 $ of a geometric progression if $ a_1 = 77 ~~ \text{and} ~~ r = 40 $.	2
4116	Find $ a_8 $ of a geometric progression if $ a_1 = 0.1111 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4117	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 0.1111 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
4118	Find $ a_4 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 4 $.	2
4119	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
4120	Find $ a_30 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.5 $.	2
4121	Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	2
4122	Find $ a_5 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2
4123	Find $ a_5 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = \dfrac{ 28 }{ 25 } $.	2
4124	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	2
4125	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $.	2
4126	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 7 } $.	2
4127	$$ a_1 = 6 ~,~ r = 3 ~,~ S_n = 6558 ~,~ n = ? $$	2
4128	$$ a_1 = 6 ~,~ r = 3 ~,~ S_n = 7 ~,~ n = ? $$	2
4129	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	2
4130	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 1 $.	2
4131	$$ a_1 = 9 ~~,~~ r = 3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4132	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 20 $.	2
4133	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 1 $.	2
4134	Find $ a_6 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1 $.	2
4135	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 80 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
4136	Find $ a_10 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
4137	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
4138	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.	2
4139	$$ a_1 = -3 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4140	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.05 $.	2
4141	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -2 $.	2
4142	Find $ a_8 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = 1.667 $.	2
4143	Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	2
4144	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
4145	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6560 ~~ \text{and} ~~ r = 2 $.	2
4146	Find $ a_2 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	2
4147	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
4148	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 10 } = 300 ~~ \text{and} ~~ a_{ 15 } = 325 $.	2
4149	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 10 } = 100 ~~ \text{and} ~~ a_{ 15 } = 125 $.	2
4150	Find $ a_9 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -4 $.	2