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
6101	Find $ a_9 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6102	$$ a_1 = 2 ~,~ r = 4 ~,~ a_n = 10 ~,~ n = ? $$	2
6103	$$ a_1 = 2 ~,~ r = 4 ~,~ a_n = 8388608 ~,~ n = ? $$	2
6104	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	2
6105	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 50 }{ 51 } $.	2
6106	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -\frac{ 1 }{ 8 } $.	2
6107	Find $ a_1 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6108	Find $ a_1 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	2
6109	Find $ a_1 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 4 $.	2
6110	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 11 ~~ \text{and} ~~ r = 2 $.	2
6111	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 0.9 $.	2
6112	Find the sum of the first $ 39 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.9 $.	2
6113	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 2 }{ 3 } ~~ \text{and} ~~ a_{ 5 } = -\frac{ 16 }{ 27 } $.	2
6114	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.75 $.	2
6115	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.75 $.	2
6116	$$ a_1 = 65000 ~,~ r = \frac{ 1 }{ 4 } ~,~ a_n = 1000000 ~,~ n = ? $$	2
6117	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -3 $.	2
6118	Find $ a_13 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6119	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 28 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6120	Find $ a_5 $ of a geometric progression if $ a_1 = -\dfrac{ 9 }{ 8 } ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	2
6121	$$ a_1 = 1 ~,~ r = 3 ~,~ S_n = 3280 ~,~ n = ? $$	2
6122	$$ a_1 = 1000 ~~,~~ r = \frac{ 7 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
6123	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 7 }{ 5 } $.	2
6124	Find $ a_10 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.4 $.	2
6125	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 1000 ~~ \text{and} ~~ a_{ 2 } = 1400 $.	2
6126	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 64 } ~~ \text{and} ~~ r = 4 $.	2
6127	$$ a_1 = \frac{ 1 }{ 64 } ~,~ r = 4 ~,~ a_n = 16 ~,~ n = ? $$	2
6128	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 17 }{ 40 } $.	2
6129	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	2
6130	Find $ a_8 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6131	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
6132	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = -4 $.	2
6133	Find $ a_8 $ of a geometric progression if $ a_1 = 135 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
6134	Find $ a_10 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6135	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6136	Find $ a_121 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.1 $.	2
6137	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.1 $.	2
6138	Find $ a_10 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 1.1 $.	2
6139	Find $ a_5 $ of a geometric progression if $ a_1 = 34 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
6140	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 34 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
6141	Find $ a_6 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2
6142	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.1 $.	2
6143	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	2
6144	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 11 } ~~ \text{and} ~~ r = \frac{ 5 }{ 11 } $.	2
6145	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	2
6146	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.6817 $.	2
6147	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.6817 $.	2
6148	Find $ a_25 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	2
6149	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6150	$$ a_1 = 78732 ~,~ r = \frac{ 1 }{ 3 } ~,~ S_n = 118096 ~,~ n = ? $$	2