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
8201	Find $ a_14 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	1
8202	Find $ a_12 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8203	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
8204	Find $ a_6 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8205	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 80 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
8206	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 50 } ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	1
8207	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $.	1
8208	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 46000 ~~ \text{and} ~~ r = \frac{ 109 }{ 100 } $.	1
8209	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 32 } ~~ \text{and} ~~ r = -2 $.	1
8210	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	1
8211	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	1
8212	Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	1
8213	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	1
8214	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 2 } ~~ \text{and} ~~ r = 6 $.	1
8215	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
8216	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
8217	Find $ a_32 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 8 $.	1
8218	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	1
8219	Find $ a_7 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	1
8220	Find $ a_70 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	1
8221	Find $ a_9 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 7 $.	1
8222	Find $ a_9 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = 7 $.	1
8223	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = \frac{ 26 }{ 25 } $.	1
8224	Find $ a_12 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -5 $.	1
8225	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 50 } $.	1
8226	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $.	1
8227	Find $ a_210000 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 25 $.	1
8228	Find the sum of the first $ 210000 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 25 $.	1
8229	Find $ a_1000000000000000 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8230	$$ a_1 = 12 ~~,~~ r = 55 ~~,~~ a_1 = ? ~~,~~ r = ? $$	1
8231	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
8232	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
8233	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 6 ~~ \text{and} ~~ a_{ 2 } = 28 $.	1
8234	Find $ a_3 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 14 }{ 3 } $.	1
8235	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 8 }{ 3 } $.	1
8236	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $.	1
8237	Find $ a_32 $ of a geometric progression if $ a_1 = 0.06 ~~ \text{and} ~~ r = 0.06 $.	1
8238	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 6 } $.	1
8239	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100000 ~~ \text{and} ~~ r = \frac{ 13 }{ 10 } $.	1
8240	$$ a_1 = 256 ~,~ r = 0.707 ~,~ a_n = 1.414 ~,~ n = ? $$	1
8241	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
8242	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 5 $.	1
8243	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 2 $.	1
8244	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 1 $.	1
8245	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
8246	Find $ a_6 $ of a geometric progression if $ a_1 = 972 ~~ \text{and} ~~ r = 3 $.	1
8247	Find $ a_5 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = 2 $.	1
8248	Find $ a_10 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = -4 $.	1
8249	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 243 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	1
8250	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 4 } ~~ \text{and} ~~ r = 2 $.	1