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
2901	Find $ a_1 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -1 $.	3
2902	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 4 ~~ \text{and} ~~ a_{ 4 } = -128 $.	3
2903	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 2 ~~ \text{and} ~~ a_{ 5 } = 64 $.	3
2904	Find first element ( $ a_1 $ ) of a geometic progression if $ r = -3 ~~ \text{and} ~~ a_{ 4 } = -81 $.	3
2905	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2906	Find $ a_5 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = 2 $.	3
2907	Find $ a_9 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $.	3
2908	Find $ a_10 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	3
2909	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	3
2910	Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	3
2911	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	3
2912	$$ a_1 = 3 ~,~ r = 10 ~,~ S_n = 33 ~,~ n = ? $$	3
2913	Find $ a_2 $ of a geometric progression if $ a_1 = 33275 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	3
2914	Find $ a_11 $ of a geometric progression if $ a_1 = 0.02 ~~ \text{and} ~~ r = -3 $.	3
2915	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 0.02 ~~ \text{and} ~~ r = -3 $.	3
2916	Find $ a_30 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	3
2917	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2918	Find $ a_12 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	3
2919	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	3
2920	$$ a_1 = 588 ~,~ r = 0.98 ~,~ a_n = 100 ~,~ n = ? $$	3
2921	Find $ a_13 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 2 $.	3
2922	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $.	3
2923	$$ a_1 = 4 ~~,~~ r = -3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	3
2924	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 9 }{ 8 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 1 }{ 4 } $.	3
2925	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	3
2926	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	3
2927	Find $ a_7 $ of a geometric progression if $ a_1 = 56 ~~ \text{and} ~~ r = 5 $.	3
2928	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 12 ~~ \text{and} ~~ a_{ 4 } = 18 $.	3
2929	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -\frac{ 49 }{ 2 } ~~ \text{and} ~~ r = -\frac{ 6 }{ 7 } $.	3
2930	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 15 ~~ \text{and} ~~ a_{ 6 } = 120 $.	3
2931	Find $ a_7 $ of a geometric progression if $ a_1 = -625 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	3
2932	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	3
2933	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 900000 ~~ \text{and} ~~ r = 1.06 $.	3
2934	Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 0.0714 $.	3
2935	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.	3
2936	Find $ a_4 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 3 $.	3
2937	Find $ a_7 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2938	Find $ a_6 $ of a geometric progression if $ a_1 = 972 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	3
2939	Find $ a_6 $ of a geometric progression if $ a_1 = 85 ~~ \text{and} ~~ r = 1.547 $.	3
2940	Find $ a_1 $ of a geometric progression if $ a_1 = 85 ~~ \text{and} ~~ r = 1.547 $.	3
2941	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	3
2942	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	3
2943	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	3
2944	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ a_{ 5 } = \frac{ 56 }{ 81 } $.	3
2945	Find $ a_1 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 5 $.	3
2946	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	3
2947	Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = 1.8 $.	3
2948	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 61 }{ 50 } $.	3
2949	Find $ a_7 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 0.75 $.	3
2950	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1875 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	3