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
3801	Find $ a_100 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.	2
3802	Find $ a_200 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.	2
3803	Find $ a_16 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 8 } ~~ \text{and} ~~ r = 2 $.	2
3804	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 8 } ~~ \text{and} ~~ r = 2 $.	2
3805	Find $ a_14 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
3806	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1024 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
3807	Find $ a_3 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 15 $.	2
3808	Find $ a_4 $ of a geometric progression if $ a_1 = 768 ~~ \text{and} ~~ r = 12 $.	2
3809	Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 6 $.	2
3810	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 8 }{ 5 } $.	2
3811	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 5000 ~~ \text{and} ~~ r = 1.03 $.	2
3812	Find $ a_2 $ of a geometric progression if $ a_1 = 1296 ~~ \text{and} ~~ r = \dfrac{ 16 }{ 81 } $.	2
3813	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1296 ~~ \text{and} ~~ r = \frac{ 16 }{ 81 } $.	2
3814	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.06 $.	2
3815	Find $ a_67 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	2
3816	Find $ a_45 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 20 $.	2
3817	Find $ a_20 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	2
3818	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 2 }{ 19 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
3819	Find $ a_10 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	2
3820	$$ a_1 = 6 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
3821	Find $ a_2 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	2
3822	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	2
3823	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	2
3824	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = \frac{ 28 }{ 25 } $.	2
3825	Find $ a_7 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = 4 $.	2
3826	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 4 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
3827	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 50500 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
3828	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 130 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	2
3829	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3830	Find $ a_10 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = -2 $.	2
3831	Find $ a_8 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3832	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 9 $.	2
3833	Find $ a_6 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 20 } $.	2
3834	Find $ a_6 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3835	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 23 } = 16 ~~ \text{and} ~~ a_{ 28 } = 24 $.	2
3836	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
3837	$$ a_1 = 3 ~,~ r = 2 ~,~ a_n = 6144 ~,~ n = ? $$	2
3838	Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 20 $.	2
3839	Find $ a_9 $ of a geometric progression if $ a_1 = -20 ~~ \text{and} ~~ r = 2 $.	2
3840	Find $ a_2 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	2
3841	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -4 $.	2
3842	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -\frac{ 13 }{ 10 } $.	2
3843	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	2
3844	Find $ a_9 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	2
3845	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3846	Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 10 $.	2
3847	Find $ a_30 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 2 $.	2
3848	Find $ a_30 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3849	$$ a_1 = 2 ~,~ r = 3 ~,~ a_n = 20 ~,~ n = ? $$	2
3850	Find $ a_1 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = -5 $.	2