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
9201	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9202	Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 0.05 $.	1
9203	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	1
9204	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	1
9205	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 5 }{ 3 } $.	1
9206	Find $ a_8 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9207	Find $ a_3 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
9208	Find $ a_14 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9209	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 2 } ~~ \text{and} ~~ r = 3 $.	1
9210	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	1
9211	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	1
9212	Find $ a_4 $ of a geometric progression if $ a_1 = 600 ~~ \text{and} ~~ r = \dfrac{ 27 }{ 25 } $.	1
9213	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 600 ~~ \text{and} ~~ r = \frac{ 27 }{ 25 } $.	1
9214	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 20 ~~ \text{and} ~~ a_{ 3 } = \frac{ 45 }{ 4 } $.	1
9215	Find $ a_16 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = \dfrac{ 26 }{ 25 } $.	1
9216	Find $ a_4 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9217	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 119 }{ 5 } $.	1
9218	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9219	Find the sum of the first $ 175 $ terms of a geometric sequence if $ a_1 = 515036 ~~ \text{and} ~~ r = 1.08 $.	1
9220	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	1
9221	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -\frac{ 2 }{ 25 } ~~ \text{and} ~~ r = -\frac{ 2 }{ 5 } $.	1
9222	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	1
9223	Find $ a_30 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = 2 $.	1
9224	Find the sum of the first $ 26 $ terms of a geometric sequence if $ a_1 = 1987 ~~ \text{and} ~~ r = 0.03 $.	1
9225	Find $ a_3 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	1
9226	Find the sum of the first $ 60 $ terms of a geometric sequence if $ a_1 = 10186 ~~ \text{and} ~~ r = 1.006 $.	1
9227	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 75 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9228	Find $ a_4 $ of a geometric progression if $ a_1 = 402050 ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.	1
9229	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9230	Find $ a_12 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
9231	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9232	Find $ a_7 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
9233	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 10 }{ 11 } $.	1
9234	$$ a_1 = 6 ~,~ r = 2 ~,~ a_n = 768 ~,~ n = ? $$	1
9235	$$ a_1 = 8 ~,~ r = 2 ~,~ S_n = 32760 ~,~ n = ? $$	1
9236	Find $ a_4 $ of a geometric progression if $ a_1 = 524059 ~~ \text{and} ~~ r = 1.02 $.	1
9237	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
9238	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
9239	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 4 $.	1
9240	Find $ a_6 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	1
9241	Find $ a_6 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	1
9242	Find $ a_15 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	1
9243	Find $ a_12 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	1
9244	Find $ a_9 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $.	1
9245	Find $ a_4 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
9246	Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $.	1
9247	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -\frac{ 2 }{ 5 } $.	1
9248	Find $ a_8 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -6 $.	1
9249	Find $ a_23 $ of a geometric progression if $ a_1 = 160000 ~~ \text{and} ~~ r = 0.1 $.	1
9250	$$ a_1 = 0.01 ~~,~~ r = 1.5 ~~,~~ a_1 = ? ~~,~~ r = ? $$	1