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
4651	Find $ a_6 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 80 } $.	2
4652	Find $ a_5 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $.	2
4653	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	2
4654	Find $ a_600 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.02 $.	2
4655	Find $ a_1500 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.02 $.	2
4656	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 12 ~~ \text{and} ~~ a_{ 3 } = \frac{ 27 }{ 4 } $.	2
4657	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 1.23 $.	2
4658	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -9 $.	2
4659	Find $ a_3 $ of a geometric progression if $ a_1 = 29000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 100 } $.	2
4660	Find $ a_15 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	2
4661	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
4662	Find $ a_2 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 100 $.	2
4663	Find the sum of the first $ 39 $ terms of a geometric sequence if $ a_1 = 1.7 ~~ \text{and} ~~ r = 1.112 $.	2
4664	Find the sum of the first $ 39 $ terms of a geometric sequence if $ a_1 = 1.7 ~~ \text{and} ~~ r = 1.114 $.	2
4665	Find the sum of the first $ 39 $ terms of a geometric sequence if $ a_1 = 1.7 ~~ \text{and} ~~ r = 1.116 $.	2
4666	Find $ a_39 $ of a geometric progression if $ a_1 = 1.7 ~~ \text{and} ~~ r = 1.114 $.	2
4667	Find $ a_25 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.114 $.	2
4668	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 1973 }{ 25 } ~~ \text{and} ~~ a_{ 10 } = \frac{ 907 }{ 2 } $.	2
4669	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1973 }{ 25 } ~~ \text{and} ~~ r = 1.214 $.	2
4670	Find $ a_8 $ of a geometric progression if $ a_1 = 2343750 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
4671	Find $ a_35 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4672	Find $ a_36 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4673	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = -5 $.	2
4674	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 409 }{ 20 } ~~ \text{and} ~~ r = 2 $.	2
4675	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 409 }{ 20 } ~~ \text{and} ~~ r = \dfrac{ 10 }{ 3 } $.	2
4676	Find $ a_8 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4677	Find $ a_4 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4678	Find $ a_4 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 0.3333 $.	2
4679	Find $ a_4 $ of a geometric progression if $ a_1 = -162 ~~ \text{and} ~~ r = 3 $.	2
4680	Find $ a_4 $ of a geometric progression if $ a_1 = -1024 ~~ \text{and} ~~ r = 4 $.	2
4681	Find $ a_4 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = 2 $.	2
4682	Find $ a_4 $ of a geometric progression if $ a_1 = 10.67 ~~ \text{and} ~~ r = 0.6667 $.	2
4683	Find $ a_9 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4684	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 11 $.	2
4685	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 81 }{ 64 } ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
4686	Find $ a_2 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $.	2
4687	Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 6 } ~~ \text{and} ~~ r = 4 $.	2
4688	Find $ a_8 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
4689	$$ a_1 = -7 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4690	$$ a_1 = -7 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4691	$$ a_1 = \frac{ 5 }{ 2 } ~~,~~ r = -\frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4692	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.	2
4693	Find $ a_97 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = 5 $.	2
4694	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = -3 $.	2
4695	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 12 $.	2
4696	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4697	Find $ a_8 $ of a geometric progression if $ a_1 = 360 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	2
4698	Find $ a_4 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.05 $.	2
4699	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 37 }{ 8 } ~~ \text{and} ~~ a_{ 5 } = 74 $.	2
4700	Find $ a_27 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	2