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
4301	Find $ a_2 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4302	Find $ a_5 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4303	Find $ a_9 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4304	Find $ a_5 $ of a geometric progression if $ a_1 = 288 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
4305	Find $ a_5 $ of a geometric progression if $ a_1 = 896 ~~ \text{and} ~~ r = -2 $.	2
4306	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
4307	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 8 } ~~ \text{and} ~~ r = \frac{ 3 }{ 8 } $.	2
4308	Find the sum of the first $ 32 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -1 $.	2
4309	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 120000 ~~ \text{and} ~~ r = 1.003 $.	2
4310	Find $ a_500 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 0.998 $.	2
4311	Find $ a_2 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4312	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 262144 ~~ \text{and} ~~ r = 8 $.	2
4313	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 38900 ~~ \text{and} ~~ r = \frac{ 103 }{ 100 } $.	2
4314	Find $ a_11 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 81 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4315	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $.	2
4316	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 63 }{ 16 } ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $.	2
4317	Find $ a_21 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	2
4318	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	2
4319	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4320	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 512 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4321	Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4322	Find $ a_3 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 50 $.	2
4323	Find $ a_10 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 2 $.	2
4324	Find $ a_9 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
4325	Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	2
4326	Find $ a_16 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 8 $.	2
4327	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	2
4328	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 5 $.	2
4329	Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 5 $.	2
4330	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -6 $.	2
4331	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $.	2
4332	Find $ a_4 $ of a geometric progression if $ a_1 = -128 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4333	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4334	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4335	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 5 }{ 3 } $.	2
4336	$$ a_1 = 4 ~,~ r = \frac{ 3 }{ 2 } ~,~ S_n = 4 ~,~ n = ? $$	2
4337	Find $ a_7 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4338	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
4339	Find $ a_3 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4340	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4341	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
4342	Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	2
4343	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
4344	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
4345	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1 $.	2
4346	Find $ a_7 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 0.3333 $.	2
4347	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 9 } ~~ \text{and} ~~ r = -\frac{ 3 }{ 2 } $.	2
4348	Find $ a_10 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 2 $.	2
4349	Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	2
4350	Find $ a_8 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2