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
9751	Find $ a_2 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	1
9752	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 9 } $.	1
9753	Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 100 } $.	1
9754	Find $ a_365 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.005 $.	1
9755	Find $ a_365 $ of a geometric progression if $ a_1 = 6144 ~~ \text{and} ~~ r = 1.005 $.	1
9756	Find $ a_365 $ of a geometric progression if $ a_1 = 37748 ~~ \text{and} ~~ r = 1.005 $.	1
9757	Find $ a_365 $ of a geometric progression if $ a_1 = 231921 ~~ \text{and} ~~ r = 1.005 $.	1
9758	Find $ a_365 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = 1.005 $.	1
9759	Find $ a_365 $ of a geometric progression if $ a_1 = 12288 ~~ \text{and} ~~ r = 1.005 $.	1
9760	Find $ a_365 $ of a geometric progression if $ a_1 = 75497 ~~ \text{and} ~~ r = 1.005 $.	1
9761	Find $ a_365 $ of a geometric progression if $ a_1 = 463849 ~~ \text{and} ~~ r = 1.005 $.	1
9762	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	1
9763	Find $ a_17 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	1
9764	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -2 $.	1
9765	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 8 } ~~ \text{and} ~~ r = -4 $.	1
9766	$$ a_1 = 1 ~,~ r = 6 ~,~ a_n = 7776 ~,~ n = ? $$	1
9767	Find $ a_151 $ of a geometric progression if $ a_1 = 75497 ~~ \text{and} ~~ r = 1.005 $.	1
9768	Find $ a_151 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = 1.005 $.	1
9769	Find $ a_151 $ of a geometric progression if $ a_1 = 10565 ~~ \text{and} ~~ r = 1.005 $.	1
9770	Find $ a_151 $ of a geometric progression if $ a_1 = 22324 ~~ \text{and} ~~ r = 1.005 $.	1
9771	Find $ a_151 $ of a geometric progression if $ a_1 = 47172 ~~ \text{and} ~~ r = 1.005 $.	1
9772	Find $ a_151 $ of a geometric progression if $ a_1 = 99677 ~~ \text{and} ~~ r = 1.005 $.	1
9773	Find $ a_151 $ of a geometric progression if $ a_1 = 210622 ~~ \text{and} ~~ r = 1.005 $.	1
9774	Find $ a_151 $ of a geometric progression if $ a_1 = 445054 ~~ \text{and} ~~ r = 1.005 $.	1
9775	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $.	1
9776	Find $ a_151 $ of a geometric progression if $ a_1 = 940420 ~~ \text{and} ~~ r = 1.005 $.	1
9777	Find $ a_604 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.005 $.	1
9778	Find $ a_10 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.005 $.	1
9779	Find $ a_20 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.005 $.	1
9780	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 1875 ~~ \text{and} ~~ a_{ 2 } = 750 $.	1
9781	$$ a_1 = 1875 ~,~ r = \frac{ 2 }{ 5 } ~,~ a_n = 3.072 ~,~ n = ? $$	1
9782	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -7 $.	1
9783	Find $ a_4 $ of a geometric progression if $ a_1 = 48000 ~~ \text{and} ~~ r = \dfrac{ 21 }{ 20 } $.	1
9784	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	1
9785	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	1
9786	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	1
9787	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
9788	Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
9789	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -\frac{ 1 }{ 7 } $.	1
9790	Find the sum of the first $ 26 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	1
9791	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = -\frac{ 3 }{ 2 } $.	1
9792	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 8 ~~ \text{and} ~~ a_{ 3 } = 16 $.	1
9793	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 1.414 $.	1
9794	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
9795	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	1
9796	$$ a_1 = 7 ~,~ r = \frac{ 2 }{ 3 } ~,~ a_n = 10 ~,~ n = ? $$	1
9797	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	1
9798	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
9799	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
9800	Find $ a_3 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 8 $.	1