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
4601	Find $ a_3 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
4602	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
4603	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	2
4604	Find $ a_5 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -2 $.	2
4605	Find $ a_9 $ of a geometric progression if $ a_1 = -19 ~~ \text{and} ~~ r = -3 $.	2
4606	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 4 ~~ \text{and} ~~ a_{ 6 } = 3072 $.	2
4607	Find $ a_2 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4608	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 10 } ~~ \text{and} ~~ r = 0.949 $.	2
4609	Find $ a_11 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
4610	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	2
4611	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4612	Find $ a_8 $ of a geometric progression if $ a_1 = 1600 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
4613	Find $ a_8 $ of a geometric progression if $ a_1 = 1600 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2
4614	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 379000 ~~ \text{and} ~~ r = 1.27 $.	2
4615	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = -2 $.	2
4616	Find $ a_8 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -1 $.	2
4617	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -1 $.	2
4618	Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 73000 ~~ \text{and} ~~ r = 1.01 $.	2
4619	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 10 }{ 3 } $.	2
4620	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 3 $.	2
4621	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = 3 $.	2
4622	Find $ a_13 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
4623	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 36 } ~~ \text{and} ~~ r = 6 $.	2
4624	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	2
4625	Find $ a_10 $ of a geometric progression if $ a_1 = 85 ~~ \text{and} ~~ r = 1.12 $.	2
4626	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
4627	Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
4628	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	2
4629	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 400 ~~ \text{and} ~~ r = -\frac{ 4 }{ 5 } $.	2
4630	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
4631	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	2
4632	Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	2
4633	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 70 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	2
4634	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4635	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4636	Find $ a_3 $ of a geometric progression if $ a_1 = 240 ~~ \text{and} ~~ r = 60 $.	2
4637	Find $ a_2 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 3 $.	2
4638	Find $ a_3 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 2 $.	2
4639	Find $ a_4 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 2 $.	2
4640	Find $ a_5 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 2 $.	2
4641	Find $ a_7 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 2 $.	2
4642	Find $ a_3 $ of a geometric progression if $ a_1 = 540 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4643	Find $ a_6 $ of a geometric progression if $ a_1 = 6561 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4644	Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -6 $.	2
4645	Find $ a_5 $ of a geometric progression if $ a_1 = 768 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
4646	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 7683 ~~ \text{and} ~~ r = 3 $.	2
4647	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 3500 ~~ \text{and} ~~ r = \frac{ 7 }{ 5 } $.	2
4648	Find $ a_12 $ of a geometric progression if $ a_1 = 0.06 ~~ \text{and} ~~ r = 1.3 $.	2
4649	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4650	$$ a_1 = \frac{ 3 }{ 2 } ~,~ r = \frac{ 1 }{ 3 } ~,~ a_n = 10 ~,~ n = ? $$	2