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
5551	Find $ a_21 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5552	Find $ a_21 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5553	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = 5 $.	2
5554	Find $ a_1 $ of a geometric progression if $ a_1 = 45 ~~ \text{and} ~~ r = 3 $.	2
5555	Find $ a_5 $ of a geometric progression if $ a_1 = 24500 ~~ \text{and} ~~ r = 0.004 $.	2
5556	Find $ a_25 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	2
5557	Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 55 }{ 2 } ~~ \text{and} ~~ r = 2 $.	2
5558	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 9 } $.	2
5559	Find $ a_9 $ of a geometric progression if $ a_1 = 232 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5560	Find $ a_8 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 3 $.	2
5561	Find $ a_8 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $.	2
5562	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	2
5563	Find $ a_8 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 3 $.	2
5564	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = 4 $.	2
5565	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = -4 $.	2
5566	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 17 }{ 10 } ~~ \text{and} ~~ r = 2 $.	2
5567	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
5568	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	2
5569	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -0.06667 $.	2
5570	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -0.06667 $.	2
5571	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -0.06667 $.	2
5572	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -0.6667 $.	2
5573	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1000000 ~~ \text{and} ~~ r = 0.85 $.	2
5574	Find $ a_5 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = -3 $.	2
5575	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 8 } ~~ \text{and} ~~ r = \frac{ 5 }{ 8 } $.	2
5576	Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 2 $.	2
5577	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -8 $.	2
5578	Find $ a_13 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	2
5579	Find $ a_10 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	2
5580	Find $ a_8 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -3 $.	2
5581	Find $ a_8 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5582	Find $ a_13 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = 2 $.	2
5583	Find $ a_7 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = -3 $.	2
5584	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
5585	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	2
5586	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -\frac{ 1 }{ 7 } $.	2
5587	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 6 }{ 5 } ~~ \text{and} ~~ r = 5 $.	2
5588	Find $ a_8 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 2 $.	2
5589	Find $ a_6 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = 0.6667 $.	2
5590	Find $ a_8 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = 6 $.	2
5591	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 5 }{ 3 } $.	2
5592	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1000 $.	2
5593	Find $ a_1 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $.	2
5594	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5595	Find $ a_2 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5596	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
5597	$$ a_1 = 12 ~~,~~ r = 5 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
5598	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = 3 $.	2
5599	Find $ a_8 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	2
5600	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	2