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
3951	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -3 $.	2
3952	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 11 ~~ \text{and} ~~ r = -5 $.	2
3953	$$ a_1 = 8 ~,~ r = 8 ~,~ a_n = 512 ~,~ n = ? $$	2
3954	$$ a_1 = 8 ~,~ r = 6 ~,~ a_n = 13436928 ~,~ n = ? $$	2
3955	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 6 $.	2
3956	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 443500 ~~ \text{and} ~~ r = 1.2 $.	2
3957	Find $ a_5 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = -2 $.	2
3958	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = \frac{ 93 }{ 100 } ~~ \text{and} ~~ r = 0.0225 $.	2
3959	Find $ a_50 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3960	Find $ a_19 $ of a geometric progression if $ a_1 = 19613 ~~ \text{and} ~~ r = 1.06 $.	2
3961	Find $ a_21 $ of a geometric progression if $ a_1 = 19613 ~~ \text{and} ~~ r = 1.06 $.	2
3962	$$ a_1 = 5 ~,~ r = 2 ~,~ S_n = 163835 ~,~ n = ? $$	2
3963	$$ a_1 = 3 ~,~ r = 3 ~,~ S_n = 2187 ~,~ n = ? $$	2
3964	$$ a_1 = 3 ~,~ r = 3 ~,~ a_n = 7 ~,~ n = ? $$	2
3965	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1024 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3966	Find $ a_8 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 6 $.	2
3967	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.005 ~~ \text{and} ~~ r = 1.2 $.	2
3968	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.005 ~~ \text{and} ~~ r = 1.1 $.	2
3969	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 6 $.	2
3970	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 495000 ~~ \text{and} ~~ r = 0.9 $.	2
3971	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 495000 ~~ \text{and} ~~ r = 0.9 $.	2
3972	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 2357 ~~ \text{and} ~~ r = 1.025 $.	2
3973	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2357 ~~ \text{and} ~~ r = 1.025 $.	2
3974	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
3975	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3976	Find $ a_8 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
3977	Find $ a_8 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
3978	Find $ a_4 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 5 $.	2
3979	Find $ a_5 $ of a geometric progression if $ a_1 = 40960 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3980	Find $ a_5 $ of a geometric progression if $ a_1 = 6800 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $.	2
3981	Find $ a_5 $ of a geometric progression if $ a_1 = 6800 ~~ \text{and} ~~ r = 30 $.	2
3982	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -\frac{ 7 }{ 3 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
3983	Find $ a_3 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3984	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.	2
3985	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3986	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 13 }{ 100 } ~~ \text{and} ~~ r = 10 $.	2
3987	Find $ a_100 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 0.95 $.	2
3988	Find $ a_20 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 0.95 $.	2
3989	Find $ a_3 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 19 }{ 20 } $.	2
3990	Find $ a_7 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 19 }{ 20 } $.	2
3991	Find $ a_15 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $.	2
3992	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 81 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
3993	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 81 } ~~ \text{and} ~~ r = 3 $.	2
3994	Find $ a_9 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	2
3995	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	2
3996	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 61 }{ 50 } $.	2
3997	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	2
3998	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	2
3999	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 80 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4000	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 6 } $.	2