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
3851	Find $ a_1 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -5 $.	2
3852	$$ a_1 = 9072 ~,~ r = \frac{ 5 }{ 6 } ~,~ a_n = 7 ~,~ n = ? $$	2
3853	$$ a_1 = 9072 ~,~ r = \frac{ 5 }{ 6 } ~,~ S_n = 7 ~,~ n = ? $$	2
3854	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 16 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
3855	$$ a_1 = 30000 ~,~ r = \frac{ 11 }{ 10 } ~,~ S_n = 222000 ~,~ n = ? $$	2
3856	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 240000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	2
3857	Find $ a_160 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -40 $.	2
3858	Find $ a_14 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	2
3859	Find $ a_13 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	2
3860	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 0.6667 $.	2
3861	Find $ a_20 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3862	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -14 ~~ \text{and} ~~ r = 3 $.	2
3863	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -5 $.	2
3864	Find $ a_5 $ of a geometric progression if $ a_1 = 24500 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 20 } $.	2
3865	Find $ a_5 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3866	Find $ a_15 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3867	$$ a_1 = 5 ~,~ r = 5 ~,~ S_n = 78125 ~,~ n = ? $$	2
3868	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3869	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 65 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2
3870	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -3 $.	2
3871	$$ a_1 = 4 ~,~ r = 2 ~,~ S_n = 1024 ~,~ n = ? $$	2
3872	Find $ a_5 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
3873	Find $ a_7 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $.	2
3874	Find $ a_25 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3875	Find $ a_8 $ of a geometric progression if $ a_1 = 9000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
3876	Find $ a_1 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	2
3877	Find $ a_2 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
3878	Find $ a_7 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3879	Find $ a_20 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3880	Find $ a_20 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 2 $.	2
3881	Find $ a_20 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3882	Find $ a_7 $ of a geometric progression if $ a_1 = 1.7 ~~ \text{and} ~~ r = 1.7 $.	2
3883	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2
3884	Find $ a_10 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 0.025 $.	2
3885	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 2600 ~~ \text{and} ~~ r = 1.4 $.	2
3886	Find $ a_12 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -2 $.	2
3887	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 30000 ~~ \text{and} ~~ r = 1.133 $.	2
3888	Find $ a_10 $ of a geometric progression if $ a_1 = 18000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
3889	Find $ a_13 $ of a geometric progression if $ a_1 = 18000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3890	Find the sum of the first $ 45 $ terms of a geometric sequence if $ a_1 = 0.0005 ~~ \text{and} ~~ r = 1.2 $.	2
3891	Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	2
3892	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	2
3893	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 61 }{ 50 } $.	2
3894	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3895	Find $ a_3 $ of a geometric progression if $ a_1 = 600 ~~ \text{and} ~~ r = 17 $.	2
3896	Find $ a_3 $ of a geometric progression if $ a_1 = 600 ~~ \text{and} ~~ r = \dfrac{ 17 }{ 100 } $.	2
3897	Find $ a_10 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	2
3898	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	2
3899	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 5 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $.	2
3900	Find $ a_7 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = -2 $.	2