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
6901	Find first element ( $ a_1 $ ) of a geometic progression if $ r = -3 ~~ \text{and} ~~ a_{ 2 } = -6 $.	1
6902	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 2 ~~ \text{and} ~~ a_{ 2 } = -8 $.	1
6903	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 2 ~~ \text{and} ~~ a_{ 4 } = -432 $.	1
6904	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 6 ~~ \text{and} ~~ a_{ 4 } = -432 $.	1
6905	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 33 }{ 100 } $.	1
6906	Find $ a_9 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6907	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.075 $.	1
6908	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
6909	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = -\frac{ 3 }{ 5 } $.	1
6910	Find $ a_5 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 2 $.	1
6911	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 131 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	1
6912	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
6913	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
6914	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
6915	Find $ a_17 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 1.75 $.	1
6916	Find $ a_4 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = 2 $.	1
6917	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $.	1
6918	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 5 } $.	1
6919	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 3 $.	1
6920	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 1 }{ 7 } $.	1
6921	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ r = 5 $.	1
6922	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	1
6923	Find $ a_5 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
6924	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 25 } ~~ \text{and} ~~ r = -5 $.	1
6925	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 11 }{ 36 } ~~ \text{and} ~~ r = -6 $.	1
6926	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
6927	Find $ a_3 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 1 $.	1
6928	Find $ a_8 $ of a geometric progression if $ a_1 = -135 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
6929	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	1
6930	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	1
6931	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	1
6932	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -20 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
6933	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 4 }{ 9 } $.	1
6934	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 9 } $.	1
6935	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 9 } $.	1
6936	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
6937	Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 49 }{ 100 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 100 } $.	1
6938	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = \frac{ 49 }{ 100 } ~~ \text{and} ~~ r = \frac{ 1 }{ 100 } $.	1
6939	$$ a_1 = 3 ~,~ r = 5 ~,~ a_n = 10 ~,~ n = ? $$	1
6940	Find $ a_7 $ of a geometric progression if $ a_1 = 67686450 ~~ \text{and} ~~ r = 1.15 $.	1
6941	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 5 }{ 7 } $.	1
6942	Find $ a_5 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1 $.	1
6943	Find $ a_5 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
6944	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = 0.03 $.	1
6945	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = \frac{ 3 }{ 100 } $.	1
6946	Find $ a_16 $ of a geometric progression if $ a_1 = 40000 ~~ \text{and} ~~ r = 1.03 $.	1
6947	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -4 $.	1
6948	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 75 ~~ \text{and} ~~ r = 0.96 $.	1
6949	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 3 }{ 11 } $.	1
6950	Find $ a_7 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 11 } $.	1