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
4701	Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	2
4702	$$ a_1 = -7 ~~,~~ r = -3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4703	Find the sum of the first $ 200 $ terms of a geometric sequence if $ a_1 = 1.067 ~~ \text{and} ~~ r = 1.15 $.	2
4704	Find $ a_10 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
4705	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 19 }{ 10 } $.	2
4706	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.5263 $.	2
4707	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 10 } $.	2
4708	Find $ a_8 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -20 $.	2
4709	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	2
4710	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3.5 ~~ \text{and} ~~ r = 0.5 $.	2
4711	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = 5 $.	2
4712	Find $ a_11 $ of a geometric progression if $ a_1 = 200000 ~~ \text{and} ~~ r = 0.94 $.	2
4713	Find $ a_48 $ of a geometric progression if $ a_1 = 1.006 ~~ \text{and} ~~ r = 1.006 $.	2
4714	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	2
4715	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -0.3854 $.	2
4716	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = -2 $.	2
4717	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 125 ~~ \text{and} ~~ a_{ 2 } = 75 $.	2
4718	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 125 ~~ \text{and} ~~ a_{ 3 } = 45 $.	2
4719	Find $ a_5 $ of a geometric progression if $ a_1 = 125 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
4720	Find $ a_30 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.05 $.	2
4721	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 2 $.	2
4722	Find $ a_5 $ of a geometric progression if $ a_1 = 8000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
4723	Find $ a_15 $ of a geometric progression if $ a_1 = 3132676 ~~ \text{and} ~~ r = 1.007 $.	2
4724	Find $ a_5 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 0.07 $.	2
4725	Find $ a_5 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.07 $.	2
4726	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 17 }{ 3 } $.	2
4727	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 1536 }{ 5 } ~~ \text{and} ~~ r = -2 $.	2
4728	Find $ a_5 $ of a geometric progression if $ a_1 = -32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
4729	Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 3 $.	2
4730	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
4731	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	2
4732	Find the sum of the first $ 37 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 7 }{ 5 } $.	2
4733	Find $ a_1 $ of a geometric progression if $ a_1 = 144 ~~ \text{and} ~~ r = -12 $.	2
4734	Find $ a_5 $ of a geometric progression if $ a_1 = 144 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 12 } $.	2
4735	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = \frac{ 43 }{ 256 } ~~ \text{and} ~~ a_{ 8 } = 172 $.	2
4736	Find $ a_25 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4737	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 80000 ~~ \text{and} ~~ r = \frac{ 103 }{ 100 } $.	2
4738	Find $ a_4 $ of a geometric progression if $ a_1 = 80000 ~~ \text{and} ~~ r = \dfrac{ 103 }{ 100 } $.	2
4739	Find $ a_7 $ of a geometric progression if $ a_1 = -\dfrac{ 7 }{ 2 } ~~ \text{and} ~~ r = 4 $.	2
4740	$$ a_1 = \frac{ 35 }{ 2 } ~,~ r = \frac{ 2 }{ 5 } ~,~ a_n = 4 ~,~ n = ? $$	2
4741	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 349 ~~ \text{and} ~~ r = 0.955 $.	2
4742	Find $ a_23 $ of a geometric progression if $ a_1 = 4000 ~~ \text{and} ~~ r = 1.25 $.	2
4743	Find the sum of the first $ 54 $ terms of a geometric sequence if $ a_1 = 800 ~~ \text{and} ~~ r = 0.96 $.	2
4744	Find $ a_1 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	2
4745	Find the sum of the first $ 10000000000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.414 $.	2
4746	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -6 ~~ \text{and} ~~ r = -\frac{ 4 }{ 3 } $.	2
4747	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	2
4748	Find $ a_4 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -3 $.	2
4749	Find $ a_19 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = 1.5 $.	2
4750	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 125 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	2