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
8151	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 33 }{ 50 } $.	1
8152	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 5 } ~~ \text{and} ~~ r = \frac{ 33 }{ 50 } $.	1
8153	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
8154	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	1
8155	Find $ a_7 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8156	Find $ a_3 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 80 $.	1
8157	Find $ a_50 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 3 $.	1
8158	Find $ a_50 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 90 $.	1
8159	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 15 $.	1
8160	Find $ a_2 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 10 $.	1
8161	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 16 ~~ \text{and} ~~ a_{ 2 } = 8 $.	1
8162	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 7 }{ 10 } $.	1
8163	$$ a_1 = 8 ~,~ r = 5 ~,~ a_n = 3125000 ~,~ n = ? $$	1
8164	$$ a_1 = \frac{ 19141 }{ 100 } ~,~ r = 1.031 ~,~ a_n = 1020 ~,~ n = ? $$	1
8165	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = 15 ~~ \text{and} ~~ a_{ 7 } = \frac{ 405 }{ 64 } $.	1
8166	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 41 }{ 10 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 87 }{ 20 } $.	1
8167	Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 41 }{ 10 } ~~ \text{and} ~~ r = 1.061 $.	1
8168	$$ a_1 = 5 ~~,~~ r = 3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	1
8169	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
8170	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1 $.	1
8171	Find $ a_6 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = -1 $.	1
8172	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 4 ~~ \text{and} ~~ a_{ 7 } = -10992 $.	1
8173	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 5 }{ 3 } $.	1
8174	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 5 }{ 3 } $.	1
8175	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	1
8176	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 3 } ~~ \text{and} ~~ r = 3 $.	1
8177	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
8178	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
8179	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 1.2 $.	1
8180	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.041 $.	1
8181	Find $ a_12 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 0.041 $.	1
8182	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.041 $.	1
8183	Find $ a_12 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = -2 $.	1
8184	Find $ a_9 $ of a geometric progression if $ a_1 = -3125 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
8185	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 250 } ~~ \text{and} ~~ r = 4 $.	1
8186	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
8187	Find the sum of the first $ 23 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
8188	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	1
8189	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 2 $.	1
8190	Find $ a_6 $ of a geometric progression if $ a_1 = -34816 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8191	Find $ a_12 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8192	Find $ a_46 $ of a geometric progression if $ a_1 = 310 ~~ \text{and} ~~ r = 0.98 $.	1
8193	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	1
8194	Find $ a_4 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
8195	Find $ a_5 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
8196	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -1 $.	1
8197	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 8 }{ 25 } ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	1
8198	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	1
8199	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	1
8200	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	1