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
6501	Find $ a_12 $ of a geometric progression if $ a_1 = 2.121 ~~ \text{and} ~~ r = 1.414 $.	2
6502	Find the sum of the first $ 9999999 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
6503	Find $ a_6 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6504	Find $ a_1 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6505	Find $ a_2 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6506	$$ a_1 = 8 ~,~ r = \frac{ 1 }{ 2 } ~,~ S_n = \frac{ 255 }{ 16 } ~,~ n = ? $$	2
6507	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 1 }{ 10 } $.	2
6508	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 60 ~~ \text{and} ~~ r = 1.75 $.	2
6509	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 21000 ~~ \text{and} ~~ r = 1.2 $.	2
6510	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 63500 ~~ \text{and} ~~ r = 1.065 $.	2
6511	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 82000 ~~ \text{and} ~~ r = 1.065 $.	2
6512	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 16770 ~~ \text{and} ~~ r = 1.065 $.	2
6513	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	2
6514	Find $ a_5 $ of a geometric progression if $ a_1 = 16770 ~~ \text{and} ~~ r = 1.065 $.	2
6515	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 9 } ~~ \text{and} ~~ r = 3 $.	2
6516	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = 2 $.	2
6517	$$ a_1 = \frac{ 3 }{ 4 } ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = \frac{ 1 }{ 96 } ~,~ n = ? $$	2
6518	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	2
6519	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 12 }{ 5 } $.	2
6520	Find $ a_6 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	2
6521	Find $ a_15 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = -2 $.	2
6522	Find $ a_6 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
6523	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -500 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2
6524	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 8 $.	2
6525	Find the sum of the first $ 42 $ terms of a geometric sequence if $ a_1 = 130000 ~~ \text{and} ~~ r = 1.1 $.	2
6526	Find $ a_5 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 49 } ~~ \text{and} ~~ r = -7 $.	2
6527	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 4000 ~~ \text{and} ~~ r = 60 $.	2
6528	$$ a_1 = 3 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = \frac{ 3 }{ 64 } ~,~ n = ? $$	2
6529	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
6530	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
6531	Find $ a_14 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -3 $.	2
6532	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.	2
6533	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	2
6534	$$ a_1 = 4 ~,~ r = 4 ~,~ S_n = 21844 ~,~ n = ? $$	2
6535	Find $ a_5 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 3 $.	2
6536	$$ a_1 = 3 ~~,~~ r = 4 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
6537	$$ a_1 = 3 ~~,~~ r = 4 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
6538	Find $ a_6 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
6539	Find $ a_8 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	2
6540	Find $ a_3 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -3 $.	2
6541	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	2
6542	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = -\frac{ 5 }{ 3 } $.	2
6543	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 3 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
6544	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
6545	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	2
6546	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	2
6547	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
6548	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -\frac{ 4 }{ 3 } ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	2
6549	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 3 $.	2
6550	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 24 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2