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
7151	Find $ a_9 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -2 $.	1
7152	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 175 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	1
7153	Find $ a_5 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 9 } $.	1
7154	Find $ a_4 $ of a geometric progression if $ a_1 = 3200 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
7155	Find $ a_6 $ of a geometric progression if $ a_1 = 3600 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
7156	Find $ a_5 $ of a geometric progression if $ a_1 = 3600 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
7157	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
7158	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 12 $.	1
7159	Find $ a_57 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -1 $.	1
7160	Find $ a_18 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 4 $.	1
7161	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 25000 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
7162	Find $ a_7 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	1
7163	Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	1
7164	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 32 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
7165	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
7166	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -6561 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
7167	$$ a_1 = 10 ~,~ r = \frac{ 5 }{ 3 } ~,~ a_n = \frac{ 156250 }{ 729 } ~,~ n = ? $$	1
7168	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	1
7169	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
7170	Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 1830 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
7171	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = -9 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
7172	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 29 }{ 50 } $.	1
7173	Find $ a_4 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
7174	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = 10 $.	1
7175	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -12 ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $.	1
7176	Find $ a_6 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	1
7177	Find $ a_3 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
7178	Find $ a_30 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 2 $.	1
7179	Find $ a_8 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 2 $.	1
7180	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 18 ~~ \text{and} ~~ a_{ 6 } = 486 $.	1
7181	$$ a_1 = 2 ~,~ r = 3 ~,~ a_n = 8 ~,~ n = ? $$	1
7182	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	1
7183	Find $ a_2 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	1
7184	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 6 } = 4 ~~ \text{and} ~~ a_{ 10 } = 16 $.	1
7185	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 4 $.	1
7186	Find $ a_6 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	1
7187	Find the sum of the first $ 101 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.5 $.	1
7188	Find $ a_15 $ of a geometric progression if $ a_1 = 37 ~~ \text{and} ~~ r = -1 $.	1
7189	Find $ a_13 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = -1 $.	1
7190	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	1
7191	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -5 $.	1
7192	Find $ a_12 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	1
7193	Find $ a_14 $ of a geometric progression if $ a_1 = 920 ~~ \text{and} ~~ r = 1.007 $.	1
7194	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 25 } ~~ \text{and} ~~ r = 1 $.	1
7195	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 25 } ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	1
7196	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 7 }{ 10 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
7197	$$ a_1 = 85 ~,~ r = \frac{ 21 }{ 20 } ~,~ S_n = \frac{ 1159029 }{ 50 } ~,~ n = ? $$	1
7198	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 2600000 ~~ \text{and} ~~ r = 0.95 $.	1
7199	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = -1.5 $.	1
7200	Find $ a_4 $ of a geometric progression if $ a_1 = -13 ~~ \text{and} ~~ r = 2 $.	1