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
11201	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = 512 ~~ \text{and} ~~ a_{ 7 } = 32768 $.	1
11202	Find $ a_1 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 20 $.	1
11203	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 1 ~~ \text{and} ~~ a_{ 5 } = 64 $.	1
11204	Find $ a_6 $ of a geometric progression if $ a_1 = 120 ~~ \text{and} ~~ r = 25.2 $.	1
11205	Find $ a_14 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $.	1
11206	Find $ a_14 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	1
11207	Find $ a_100000 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
11208	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 467426 ~~ \text{and} ~~ r = 0.83 $.	1
11209	Find the sum of the first $ 99 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $.	1
11210	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = -12 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
11211	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
11212	Find the sum of the first $ 66 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
11213	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
11214	Find the sum of the first $ 9223372036854775807 $ terms of a geometric sequence if $ a_1 = 150 ~~ \text{and} ~~ r = -0.4 $.	1
11215	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	1
11216	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ r = 2 $.	1
11217	Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 8 }{ 3 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
11218	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
11219	Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
11220	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
11221	Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
11222	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 0.95 $.	1
11223	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = -3 $.	1
11224	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 1 $.	1
11225	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	1
11226	Find $ a_14 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
11227	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6500 ~~ \text{and} ~~ r = \frac{ 107 }{ 100 } $.	1
11228	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6955 ~~ \text{and} ~~ r = 1.07 $.	1
11229	Find $ a_100 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 0.367 $.	1
11230	Find $ a_100 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 0.367 $.	1
11231	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 12 $.	1
11232	Find $ a_4 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
11233	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
11234	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 3 ~~ \text{and} ~~ a_{ 4 } = 125 $.	1
11235	Find $ a_9999 $ of a geometric progression if $ a_1 = 500000 ~~ \text{and} ~~ r = 0.99 $.	1
11236	Find $ a_999 $ of a geometric progression if $ a_1 = 500000 ~~ \text{and} ~~ r = 0.99 $.	1
11237	Find $ a_6 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
11238	Find $ a_6 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	1
11239	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
11240	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 9 $.	1
11241	Find $ a_4 $ of a geometric progression if $ a_1 = 222 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	1
11242	$$ a_1 = 1 ~,~ r = 3 ~,~ S_n = 22 ~,~ n = ? $$	1
11243	$$ a_1 = 12000 ~,~ r = \frac{ 11 }{ 10 } ~,~ a_n = 100 ~,~ n = ? $$	1
11244	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = -7 ~~ \text{and} ~~ r = 4 $.	1
11245	Find $ a_3 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	1
11246	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
11247	Find $ a_9 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -4 $.	1
11248	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 243 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
11249	Find $ a_9 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
11250	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1