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
9351	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 0.00075 ~~ \text{and} ~~ r = \frac{ 13 }{ 10 } $.	1
9352	Find $ a_20 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 50 } ~~ \text{and} ~~ r = -2 $.	1
9353	Find $ a_9 $ of a geometric progression if $ a_1 = 0.02 ~~ \text{and} ~~ r = -2 $.	1
9354	Find $ a_4 $ of a geometric progression if $ a_1 = 0.02 ~~ \text{and} ~~ r = -2 $.	1
9355	Find $ a_15 $ of a geometric progression if $ a_1 = 0.02 ~~ \text{and} ~~ r = -3 $.	1
9356	Find $ a_12 $ of a geometric progression if $ a_1 = 0.02 ~~ \text{and} ~~ r = -3 $.	1
9357	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
9358	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9359	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	1
9360	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -1 $.	1
9361	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $.	1
9362	Find $ a_3 $ of a geometric progression if $ a_1 = 18000 ~~ \text{and} ~~ r = 0.15 $.	1
9363	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1024 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
9364	Find $ a_10 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
9365	Find $ a_1 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9366	Find $ a_11 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 12 $.	1
9367	Find $ a_11 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 3 $.	1
9368	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -12 $.	1
9369	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 33 }{ 5 } ~~ \text{and} ~~ r = -5 $.	1
9370	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 25 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	1
9371	$$ a_1 = 27 ~,~ r = \frac{ 1 }{ 3 } ~,~ a_n = \frac{ 1 }{ 729 } ~,~ n = ? $$	1
9372	Find $ a_9 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9373	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
9374	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 729 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9375	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 32 ~~ \text{and} ~~ a_{ 10 } = 1024 $.	1
9376	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 26 ~~ \text{and} ~~ a_{ 13 } = 4096 $.	1
9377	$$ a_1 = 2.072 ~,~ r = 1.882 ~,~ a_n = 7 ~,~ n = ? $$	1
9378	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 2.072 ~~ \text{and} ~~ a_{ 13 } = 4096 $.	1
9379	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 10 $.	1
9380	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = 10 $.	1
9381	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 5 $.	1
9382	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9383	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9384	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	1
9385	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 60 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $.	1
9386	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
9387	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 9 } ~~ \text{and} ~~ r = -3 $.	1
9388	Find $ a_26 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 50 } ~~ \text{and} ~~ r = 2 $.	1
9389	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	1
9390	Find $ a_12 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -0.3333 $.	1
9391	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 8 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
9392	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9393	$$ a_1 = 2 ~~,~~ r = -3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	1
9394	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 11 }{ 100 } ~~ \text{and} ~~ r = \frac{ 19 }{ 2 } $.	1
9395	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 18 ~~ \text{and} ~~ a_{ 3 } = 54 $.	1
9396	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = 3 $.	1
9397	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	1
9398	Find $ a_1 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 7 } $.	1
9399	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 250 ~~ \text{and} ~~ r = -\frac{ 3 }{ 5 } $.	1
9400	Find $ a_5 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 9 } $.	1