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
5501	Find $ a_9 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = 2 $.	2
5502	Find $ a_6 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -1 $.	2
5503	Find $ a_7 $ of a geometric progression if $ a_1 = -13 ~~ \text{and} ~~ r = -2 $.	2
5504	Find $ a_4 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5505	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5506	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5507	Find $ a_8 $ of a geometric progression if $ a_1 = 6561 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
5508	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -6 $.	2
5509	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 8 }{ 3 } $.	2
5510	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	2
5511	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -\frac{ 8 }{ 5 } $.	2
5512	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 12 $.	2
5513	Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5514	Find $ a_42 $ of a geometric progression if $ a_1 = 313 ~~ \text{and} ~~ r = -6 $.	2
5515	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5516	Find $ a_21 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	2
5517	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 16 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5518	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
5519	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 7.2 ~~ \text{and} ~~ a_{ 4 } = 5.832 $.	2
5520	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 0.9 $.	2
5521	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 1 $.	2
5522	Find $ a_29 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
5523	Find $ a_29 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
5524	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	2
5525	Find $ a_11 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 36 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	2
5526	Find $ a_5 $ of a geometric progression if $ a_1 = 1500 ~~ \text{and} ~~ r = 2 $.	2
5527	Find $ a_5 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -2 $.	2
5528	Find $ a_8 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -2 $.	2
5529	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 0.4 $.	2
5530	Find $ a_7 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5531	Find $ a_11 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -3 $.	2
5532	Find $ a_5 $ of a geometric progression if $ a_1 = 7680 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5533	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = 2 $.	2
5534	Find $ a_4 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 0.1 $.	2
5535	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -2 $.	2
5536	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 1.05 ~~ \text{and} ~~ a_{ 10 } = 1258 $.	2
5537	Find $ a_40 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.129 $.	2
5538	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = 4 $.	2
5539	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = 64 ~~ \text{and} ~~ a_{ 7 } = 8 $.	2
5540	Find $ a_14 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	2
5541	Find the sum of the first $ 99999999999 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5542	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	2
5543	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5544	Find $ a_31 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 1.316 $.	2
5545	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 171 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
5546	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 2 $.	2
5547	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5548	Find $ a_5 $ of a geometric progression if $ a_1 = -16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5549	Find $ a_10 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.	2
5550	Find $ a_21 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2