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
5101	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 80 ~~ \text{and} ~~ a_{ 3 } = 120 $.	2
5102	Find $ a_10 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	2
5103	Find $ a_6 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
5104	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 48 ~~ \text{and} ~~ a_{ 4 } = 75 $.	2
5105	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 64 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	2
5106	Find $ a_7 $ of a geometric progression if $ a_1 = 160 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5107	Find $ a_4 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5108	Find $ a_6 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5109	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 27 ~~ \text{and} ~~ a_{ 4 } = 8 $.	2
5110	Find the sum of the first $ 1000000 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = 0.6667 $.	2
5111	Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	2
5112	Find the sum of the first $ 10000 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
5113	Find $ a_11 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 3 $.	2
5114	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = 1.1 $.	2
5115	Find $ a_10 $ of a geometric progression if $ a_1 = 2187 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
5116	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	2
5117	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -4 $.	2
5118	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 5 $.	2
5119	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
5120	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 21 ~~ \text{and} ~~ r = -5 $.	2
5121	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 3 $.	2
5122	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	2
5123	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 4 }{ 9 } $.	2
5124	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 103000 ~~ \text{and} ~~ r = 0.99 $.	2
5125	Find $ a_7 $ of a geometric progression if $ a_1 = 120 ~~ \text{and} ~~ r = 1.1 $.	2
5126	$$ a_1 = \frac{ 1 }{ 2 } ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = \frac{ 1 }{ 512 } ~,~ n = ? $$	2
5127	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5128	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5129	$$ a_1 = \frac{ 1 }{ 2 } ~~,~~ r = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
5130	Find $ a_14 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	2
5131	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
5132	Find $ a_13 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	2
5133	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 1 ~~ \text{and} ~~ a_{ 21 } = 10 $.	2
5134	$$ a_1 = 1 ~,~ r = 1.122 ~,~ a_n = 200 ~,~ n = ? $$	2
5135	$$ a_1 = 1 ~,~ r = 1.122 ~,~ a_n = 100 ~,~ n = ? $$	2
5136	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -\frac{ 3 }{ 2 } ~~ \text{and} ~~ r = 2.5 $.	2
5137	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -\frac{ 3 }{ 2 } ~~ \text{and} ~~ r = 0.66 $.	2
5138	Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5139	Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	2
5140	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 13 }{ 10 } $.	2
5141	Find $ a_2 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 6 $.	2
5142	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
5143	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = 1.003 $.	2
5144	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	2
5145	Find the sum of the first $ 164 $ terms of a geometric sequence if $ a_1 = 1778 ~~ \text{and} ~~ r = 1.016 $.	2
5146	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
5147	Find $ a_15 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = 2 $.	2
5148	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	2
5149	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	2
5150	Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 11 } $.	2