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
4351	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
4352	Find $ a_4 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4353	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
4354	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $.	2
4355	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -1 $.	2
4356	Find $ a_7 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 0.25 $.	2
4357	Find $ a_7 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = -0.25 $.	2
4358	Find $ a_7 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = -0.5 $.	2
4359	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $.	2
4360	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 0.1667 $.	2
4361	Find $ a_12 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -4 $.	2
4362	$$ a_1 = 3 ~,~ r = 4 ~,~ a_n = 3145728 ~,~ n = ? $$	2
4363	Find $ a_11 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4364	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 32 } ~~ \text{and} ~~ r = -2 $.	2
4365	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 32 } ~~ \text{and} ~~ r = -2 $.	2
4366	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 32 } ~~ \text{and} ~~ r = -2 $.	2
4367	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -2 $.	2
4368	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = 0.5 $.	2
4369	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
4370	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 32 $.	2
4371	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	2
4372	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4373	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 2 $.	2
4374	Find $ a_35 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	2
4375	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	2
4376	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	2
4377	Find $ a_15 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 2 $.	2
4378	Find $ a_8 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	2
4379	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 3 } = \frac{ 16 }{ 3 } $.	2
4380	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
4381	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
4382	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 600 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	2
4383	Find $ a_11 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	2
4384	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	2
4385	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
4386	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
4387	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	2
4388	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 6 $.	2
4389	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	2
4390	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	2
4391	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $.	2
4392	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 120000 ~~ \text{and} ~~ r = \frac{ 27 }{ 25 } $.	2
4393	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.	2
4394	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 1.05 $.	2
4395	Find $ a_30 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 1.05 $.	2
4396	Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -2 $.	2
4397	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100000 ~~ \text{and} ~~ r = \frac{ 3 }{ 10 } $.	2
4398	Find $ a_5 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = 0.707 $.	2
4399	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = 0.7071 $.	2
4400	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	2