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
10251	Find $ a_37 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10252	Find $ a_3 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
10253	Find $ a_8 $ of a geometric progression if $ a_1 = 82 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10254	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -6 $.	1
10255	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	1
10256	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 409 }{ 20 } ~~ \text{and} ~~ r = \dfrac{ 111 }{ 25 } $.	1
10257	Find $ a_15 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.5 $.	1
10258	Find $ a_13 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.5 $.	1
10259	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
10260	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 375 }{ 2 } ~~ \text{and} ~~ r = -5 $.	1
10261	Find $ a_12 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = -0.001 $.	1
10262	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 864 }{ 5 } ~~ \text{and} ~~ r = 6 $.	1
10263	Find $ a_12 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = -0.01 $.	1
10264	Find $ a_4 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10265	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
10266	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -3 $.	1
10267	Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	1
10268	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
10269	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	1
10270	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 3 $.	1
10271	Find $ a_14 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.5 $.	1
10272	Find $ a_7 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10273	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	1
10274	Find $ a_4 $ of a geometric progression if $ a_1 = 0.1 ~~ \text{and} ~~ r = 4 $.	1
10275	$$ a_1 = \frac{ 1 }{ 10 } ~~,~~ r = 4 ~~,~~ a_1 = ? ~~,~~ r = ? $$	1
10276	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0.5 ~~ \text{and} ~~ r = \frac{ 5 }{ 9 } $.	1
10277	Find $ a_10 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 8 $.	1
10278	Find $ a_10 $ of a geometric progression if $ a_1 = 729 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
10279	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.97 $.	1
10280	Find $ a_1 $ of a geometric progression if $ a_1 = 58 ~~ \text{and} ~~ r = 2 $.	1
10281	Find the sum of the first $ 22 $ terms of a geometric sequence if $ a_1 = 60 ~~ \text{and} ~~ r = 1.08 $.	1
10282	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	1
10283	$$ a_1 = 70 ~,~ r = 5 ~,~ S_n = 27343750 ~,~ n = ? $$	1
10284	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -1 $.	1
10285	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -1 $.	1
10286	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 72 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
10287	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 4 $.	1
10288	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	1
10289	$$ a_1 = 2500 ~,~ r = \frac{ 4 }{ 5 } ~,~ S_n = \frac{ 16384 }{ 25 } ~,~ n = ? $$	1
10290	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2500 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	1
10291	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 10000 ~~ \text{and} ~~ a_{ 3 } = 400 $.	1
10292	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = 2 $.	1
10293	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	1
10294	Find $ a_100 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 0.0001 $.	1
10295	Find $ a_26 $ of a geometric progression if $ a_1 = 112000 ~~ \text{and} ~~ r = 1.18 $.	1
10296	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	1
10297	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.96 $.	1
10298	Find $ a_2 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 5 $.	1
10299	Find $ a_4 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10300	Find $ a_3 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 10 $.	1