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
5401	Find $ a_3 $ of a geometric progression if $ a_1 = 100000 ~~ \text{and} ~~ r = \dfrac{ 99 }{ 100 } $.	2
5402	Find $ a_7 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = -2 $.	2
5403	Find $ a_8 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
5404	Find $ a_7 $ of a geometric progression if $ a_1 = -96 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 6 } $.	2
5405	Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 100 } $.	2
5406	Find $ a_7 $ of a geometric progression if $ a_1 = 729 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 10 } $.	2
5407	Find $ a_7 $ of a geometric progression if $ a_1 = 729 ~~ \text{and} ~~ r = -0.03 $.	2
5408	Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	2
5409	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -4 $.	2
5410	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 50 } $.	2
5411	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 50 } $.	2
5412	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 50 } $.	2
5413	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 50 } $.	2
5414	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 50 } $.	2
5415	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 50 } $.	2
5416	Find $ a_15 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $.	2
5417	Find $ a_15 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	2
5418	Find $ a_5 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 113 }{ 100 } $.	2
5419	Find $ a_7 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = -2 $.	2
5420	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 30 $.	2
5421	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $.	2
5422	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5423	Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 5 $.	2
5424	$$ a_1 = 10 ~,~ r = 1.01 ~,~ S_n = \frac{ 2888 }{ 25 } ~,~ n = ? $$	2
5425	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 24 ~~ \text{and} ~~ a_{ 6 } = 48 $.	2
5426	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 3 } $.	2
5427	Find $ a_6 $ of a geometric progression if $ a_1 = 84.69 ~~ \text{and} ~~ r = 1.547 $.	2
5428	Find $ a_2 $ of a geometric progression if $ a_1 = 85 ~~ \text{and} ~~ r = 1.547 $.	2
5429	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -\frac{ 3 }{ 5 } $.	2
5430	Find $ a_6 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 4 $.	2
5431	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5432	Find $ a_7 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
5433	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 150 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	2
5434	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2
5435	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
5436	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 6 } ~~ \text{and} ~~ r = 5 $.	2
5437	Find $ a_10 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 54 $.	2
5438	$$ a_1 = 15 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = \frac{ 15 }{ 1024 } ~,~ n = ? $$	2
5439	Find $ a_4 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
5440	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 39 } = 11 ~~ \text{and} ~~ a_{ 37 } = 5 $.	2
5441	Find $ a_50 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	2
5442	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 59 ~~ \text{and} ~~ a_{ 8 } = 118 $.	2
5443	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 59 ~~ \text{and} ~~ a_{ 8 } = 118 $.	2
5444	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
5445	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 0.0625 ~~ \text{and} ~~ r = -2 $.	2
5446	Find $ a_2 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
5447	Find $ a_30 $ of a geometric progression if $ a_1 = 462 ~~ \text{and} ~~ r = 9 $.	2
5448	Find $ a_1 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.	2
5449	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
5450	Find the sum of the first $ 504 $ terms of a geometric sequence if $ a_1 = 503.5 ~~ \text{and} ~~ r = 1.007 $.	2