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
5301	Find $ a_5 $ of a geometric progression if $ a_1 = 3645 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
5302	Find $ a_4 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 0.125 $.	2
5303	$$ a_1 = 10 ~,~ r = \frac{ 61 }{ 50 } ~,~ S_n = 10 ~,~ n = ? $$	2
5304	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
5305	Find the sum of the first $ 24 $ terms of a geometric sequence if $ a_1 = 1300 ~~ \text{and} ~~ r = 1.015 $.	2
5306	Find the sum of the first $ 9999 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5307	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -36 $.	2
5308	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 12 } $.	2
5309	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 0.95 $.	2
5310	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 0.95 $.	2
5311	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
5312	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
5313	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 175 }{ 2 } $.	2
5314	Find $ a_3 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 5 $.	2
5315	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
5316	Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = -13.75 $.	2
5317	Find $ a_21 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5318	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
5319	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	2
5320	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	2
5321	Find $ a_15 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $.	2
5322	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 6 $.	2
5323	$$ a_1 = 20 ~,~ r = \frac{ 7 }{ 8 } ~,~ S_n = \frac{ 319 }{ 2 } ~,~ n = ? $$	2
5324	Find $ a_1 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.	2
5325	Find $ a_7 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5326	Find $ a_7 $ of a geometric progression if $ a_1 = -400 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $.	2
5327	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2
5328	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	2
5329	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
5330	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 6 $.	2
5331	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -6 $.	2
5332	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 13 $.	2
5333	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -9 ~~ \text{and} ~~ r = -5 $.	2
5334	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = 8 $.	2
5335	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 25000 ~~ \text{and} ~~ r = \frac{ 33 }{ 25 } $.	2
5336	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 25000 ~~ \text{and} ~~ r = \frac{ 33 }{ 25 } $.	2
5337	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 25000 ~~ \text{and} ~~ r = 0.32 $.	2
5338	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 3 $.	2
5339	Find the sum of the first $ 200 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 0.7 $.	2
5340	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 27 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
5341	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 9 }{ 4 } ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
5342	Find $ a_1 $ of a geometric progression if $ a_1 = 99 ~~ \text{and} ~~ r = 10 $.	2
5343	Find $ a_14 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5344	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
5345	$$ a_1 = 60 ~,~ r = \frac{ 5 }{ 2 } ~,~ a_n = 40 ~,~ n = ? $$	2
5346	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 32 } ~~ \text{and} ~~ r = -4 $.	2
5347	Find $ a_37 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 2.8 $.	2
5348	Find $ a_16 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	2
5349	Find $ a_8 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5350	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 2 }{ 5 } ~~ \text{and} ~~ r = 5 $.	2