Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
5801	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $.	2
5802	Find $ a_14 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	2
5803	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 0.01093 ~~ \text{and} ~~ a_{ 37 } = 0.04371 $.	2
5804	Find the sum of the first $ 37 $ terms of a geometric sequence if $ a_1 = 0.01093 ~~ \text{and} ~~ r = 1.039 $.	2
5805	Find the sum of the first $ 999999999 $ terms of a geometric sequence if $ a_1 = \frac{ 6 }{ 5 } ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2
5806	Find $ a_2 $ of a geometric progression if $ a_1 = 48 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5807	Find $ a_6 $ of a geometric progression if $ a_1 = 7000000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
5808	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	2
5809	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 29000 ~~ \text{and} ~~ r = 1.05 $.	2
5810	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -\frac{ 189 }{ 16 } ~~ \text{and} ~~ r = 2 $.	2
5811	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 0.73 $.	2
5812	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 85 ~~ \text{and} ~~ a_{ 2 } = \frac{ 907 }{ 10 } $.	2
5813	Find $ a_65 $ of a geometric progression if $ a_1 = 85 ~~ \text{and} ~~ r = 1.067 $.	2
5814	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.005 $.	2
5815	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 3 }{ 4 } ~~ \text{and} ~~ a_{ 4 } = 324 $.	2
5816	$$ a_1 = 2 ~,~ r = 5 ~,~ a_n = 156250 ~,~ n = ? $$	2
5817	$$ a_1 = 2 ~,~ r = 3 ~,~ a_n = 486 ~,~ n = ? $$	2
5818	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
5819	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
5820	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $.	2
5821	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
5822	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
5823	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -4 $.	2
5824	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ r = 2 $.	2
5825	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	2
5826	Find $ a_5 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 100 } $.	2
5827	Find $ a_5 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 0.01 $.	2
5828	Find $ a_244 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	2
5829	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	2
5830	Find $ a_6 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	2
5831	Find $ a_5 $ of a geometric progression if $ a_1 = 48 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5832	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5833	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 50000 ~~ \text{and} ~~ r = 1.04 $.	2
5834	Find $ a_2 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = \dfrac{ 26 }{ 25 } $.	2
5835	Find $ a_4 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = \dfrac{ 26 }{ 25 } $.	2
5836	Find $ a_10 $ of a geometric progression if $ a_1 = 66 ~~ \text{and} ~~ r = 2 $.	2
5837	Find $ a_7 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 4 $.	2
5838	Find $ a_6 $ of a geometric progression if $ a_1 = 240 ~~ \text{and} ~~ r = -2 $.	2
5839	Find $ a_5 $ of a geometric progression if $ a_1 = 3600 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5840	Find $ a_30 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 50 } ~~ \text{and} ~~ r = 2 $.	2
5841	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -5 $.	2
5842	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -5 $.	2
5843	Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -5 $.	2
5844	Find $ a_9 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $.	2
5845	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
5846	Find $ a_3 $ of a geometric progression if $ a_1 = 18000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 20 } $.	2
5847	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 18000 ~~ \text{and} ~~ r = -\frac{ 3 }{ 20 } $.	2
5848	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -\frac{ 2 }{ 5 } ~~ \text{and} ~~ r = 5 $.	2
5849	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
5850	Find $ a_4 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 6 $.	2