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
5701	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
5702	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
5703	Find $ a_5 $ of a geometric progression if $ a_1 = 0.125 ~~ \text{and} ~~ r = 4 $.	2
5704	$$ a_1 = 2 ~,~ r = 4 ~,~ a_n = 28 ~,~ n = ? $$	2
5705	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = \frac{ 1 }{ 9 } $.	2
5706	Find $ a_8 $ of a geometric progression if $ a_1 = -16 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	2
5707	Find $ a_6 $ of a geometric progression if $ a_1 = 4000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5708	Find $ a_13 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	2
5709	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
5710	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
5711	Find $ a_3 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 3 $.	2
5712	Find $ a_3 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
5713	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 1.05 $.	2
5714	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3125 }{ 96 } ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $.	2
5715	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $.	2
5716	Find $ a_11 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5717	Find $ a_30 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
5718	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 320 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5719	$$ a_1 = 6 ~,~ r = \frac{ 1 }{ 3 } ~,~ a_n = \frac{ 2 }{ 2187 } ~,~ n = ? $$	2
5720	Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 1830 ~~ \text{and} ~~ r = 0.1 $.	2
5721	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
5722	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = -10 $.	2
5723	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
5724	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
5725	Find $ a_7 $ of a geometric progression if $ a_1 = 0.5 ~~ \text{and} ~~ r = 0.1 $.	2
5726	Find $ a_6 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2
5727	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 6 $.	2
5728	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -2.236 $.	2
5729	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -16 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5730	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.8 ~~ \text{and} ~~ r = 1.2 $.	2
5731	Find the sum of the first $ 90 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = 2 $.	2
5732	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = 2 $.	2
5733	$$ a_1 = 30 ~,~ r = 2 ~,~ S_n = 10000 ~,~ n = ? $$	2
5734	Find $ a_8385143 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 2 $.	2
5735	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	2
5736	$$ a_1 = 5 ~,~ r = 3 ~,~ a_n = 32805 ~,~ n = ? $$	2
5737	Find $ a_3 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 12 $.	2
5738	Find the sum of the first $ 33 $ terms of a geometric sequence if $ a_1 = 483 ~~ \text{and} ~~ r = -21 $.	2
5739	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 4 $.	2
5740	Find $ a_8 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
5741	Find $ a_6 $ of a geometric progression if $ a_1 = 16000000 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	2
5742	Find $ a_10 $ of a geometric progression if $ a_1 = 4096 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
5743	Find $ a_729 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $.	2
5744	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
5745	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 15 }{ 2 } $.	2
5746	Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 17 }{ 2 } $.	2
5747	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
5748	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
5749	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = \frac{ 9 }{ 4 } ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
5750	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -3 $.	2