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
2851	Find $ a_5 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	3
2852	Find $ a_100 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 0.5 $.	3
2853	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	3
2854	Find $ a_26 $ of a geometric progression if $ a_1 = 4210 ~~ \text{and} ~~ r = 1.045 $.	3
2855	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 4 } $.	3
2856	Find $ a_9 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	3
2857	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $.	3
2858	Find $ a_17 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	3
2859	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 35000 ~~ \text{and} ~~ r = 1.06 $.	3
2860	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2861	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 265909000 ~~ \text{and} ~~ r = 2 $.	3
2862	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2863	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2864	Find the sum of the first $ 28 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2865	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 77 ~~ \text{and} ~~ a_{ 3 } = 226 $.	3
2866	Find $ a_2 $ of a geometric progression if $ a_1 = 226 ~~ \text{and} ~~ r = 3.08 $.	3
2867	Find $ a_5 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 3.08 $.	3
2868	Find $ a_6 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 3.08 $.	3
2869	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	3
2870	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 5 }{ 6 } $.	3
2871	Find $ a_3 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2872	Find $ a_40 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.15 $.	3
2873	Find $ a_40 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.115 $.	3
2874	$$ a_1 = 17 ~,~ r = 5 ~,~ a_n = 10 ~,~ n = ? $$	3
2875	Find $ a_300 $ of a geometric progression if $ a_1 = 300 ~~ \text{and} ~~ r = 1.015 $.	3
2876	Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 0.4 $.	3
2877	Find $ a_10 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 4 $.	3
2878	Find $ a_4 $ of a geometric progression if $ a_1 = -768 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	3
2879	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 36 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2880	Find $ a_5 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 2 $.	3
2881	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 2 $.	3
2882	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 2600000 ~~ \text{and} ~~ r = \frac{ 19 }{ 20 } $.	3
2883	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -4 $.	3
2884	Find $ a_30 $ of a geometric progression if $ a_1 = 67900 ~~ \text{and} ~~ r = 0.943 $.	3
2885	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	3
2886	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	3
2887	Find $ a_16 $ of a geometric progression if $ a_1 = 162 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	3
2888	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 1 }{ 7 } $.	3
2889	Find $ a_5 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	3
2890	Find $ a_12 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	3
2891	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	3
2892	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	3
2893	Find $ a_11 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	3
2894	Find $ a_16999 $ of a geometric progression if $ a_1 = 9.8 ~~ \text{and} ~~ r = 3.13 $.	3
2895	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 120000 ~~ \text{and} ~~ r = 1.1 $.	3
2896	Find $ a_29 $ of a geometric progression if $ a_1 = 600000 ~~ \text{and} ~~ r = 1.1 $.	3
2897	Find $ a_100 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 49 }{ 50 } $.	3
2898	Find $ a_150 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 49 }{ 50 } $.	3
2899	Find $ a_110 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 49 }{ 50 } $.	3
2900	Find the sum of the first $ 130 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = \frac{ 49 }{ 50 } $.	3