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
5451	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	2
5452	Find $ a_4 $ of a geometric progression if $ a_1 = 100000 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.	2
5453	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
5454	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	2
5455	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -20 $.	2
5456	Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -5 $.	2
5457	$$ a_1 = 4 ~,~ r = 2 ~,~ S_n = 16384 ~,~ n = ? $$	2
5458	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.1 $.	2
5459	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 57 } ~~ \text{and} ~~ r = 2 $.	2
5460	Find $ a_12 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 2 $.	2
5461	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 30000 ~~ \text{and} ~~ r = 1.03 $.	2
5462	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5463	$$ a_1 = 43 ~~,~~ r = 1 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
5464	Find $ a_12 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 0.75 $.	2
5465	Find $ a_11 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 0.75 $.	2
5466	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 0.3333 $.	2
5467	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 15 ~~ \text{and} ~~ a_{ 4 } = 9375 $.	2
5468	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 6000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	2
5469	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	2
5470	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 5000 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	2
5471	Find $ a_4 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.	2
5472	$$ a_1 = 4 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = 12 ~,~ n = ? $$	2
5473	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
5474	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $.	2
5475	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	2
5476	Find $ a_4 $ of a geometric progression if $ a_1 = -12 ~~ \text{and} ~~ r = -3 $.	2
5477	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = 4 $.	2
5478	$$ a_1 = 0 ~~,~~ r = 3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
5479	Find $ a_5 $ of a geometric progression if $ a_1 = -\dfrac{ 449 }{ 7 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
5480	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
5481	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 4 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
5482	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	2
5483	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
5484	Find $ a_8 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	2
5485	Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 12 $.	2
5486	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
5487	Find $ a_4 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5488	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	2
5489	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5490	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5491	Find $ a_7 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
5492	Find $ a_10 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -4 $.	2
5493	Find $ a_9 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $.	2
5494	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
5495	Find $ a_11 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	2
5496	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
5497	Find $ a_6 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = -3 $.	2
5498	Find $ a_11 $ of a geometric progression if $ a_1 = -13 ~~ \text{and} ~~ r = -2 $.	2
5499	Find $ a_10 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 2 $.	2
5500	Find $ a_11 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = -3 $.	2