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
4401	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	2
4402	Find $ a_8 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = 2 $.	2
4403	Find $ a_12 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -3 $.	2
4404	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1296 ~~ \text{and} ~~ r = -\frac{ 1 }{ 6 } $.	2
4405	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
4406	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -81 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	2
4407	Find $ a_5 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = \dfrac{ 27 }{ 25 } $.	2
4408	Find $ a_11 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 8 } ~~ \text{and} ~~ r = 3 $.	2
4409	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	2
4410	Find $ a_16 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
4411	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
4412	Find $ a_4 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 1.5 $.	2
4413	Find $ a_6 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 1.5 $.	2
4414	Find $ a_16 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
4415	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
4416	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 1.2 $.	2
4417	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 1.2 $.	2
4418	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 13 }{ 10 } $.	2
4419	Find $ a_5 $ of a geometric progression if $ a_1 = 162 ~~ \text{and} ~~ r = 3 $.	2
4420	$$ a_1 = 2 ~,~ r = 3 ~,~ a_n = 10 ~,~ n = ? $$	2
4421	Find $ a_6 $ of a geometric progression if $ a_1 = 625 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
4422	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -2 $.	2
4423	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4424	Find first element ( $ a_1 $ ) of a geometic progression if $ r = -2 ~~ \text{and} ~~ a_{ 3 } = 8 $.	2
4425	$$ a_1 = 6 ~~,~~ r = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
4426	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 51 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 8 }{ 5 } $.	2
4427	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
4428	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 10 $.	2
4429	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	2
4430	Find the sum of the first $ 60 $ terms of a geometric sequence if $ a_1 = 90 ~~ \text{and} ~~ r = 1.1 $.	2
4431	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = 1.13 $.	2
4432	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = 1.03 $.	2
4433	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0.04371 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	2
4434	$$ a_1 = 0.04371 ~,~ r = \frac{ 11 }{ 10 } ~,~ S_n = 1 ~,~ n = ? $$	2
4435	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 81 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	2
4436	Find $ a_15 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	2
4437	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 3 } = -54 $.	2
4438	Find $ a_14 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	2
4439	Find $ a_1 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -3 $.	2
4440	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 19741 ~~ \text{and} ~~ r = 1.025 $.	2
4441	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	2
4442	Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -5 $.	2
4443	Find $ a_6 $ of a geometric progression if $ a_1 = 729 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
4444	Find $ a_11 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 2 $.	2
4445	Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
4446	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = 70 ~~ \text{and} ~~ a_{ 7 } = \frac{ 35 }{ 4 } $.	2
4447	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
4448	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 0.1 $.	2
4449	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 46 ~~ \text{and} ~~ a_{ 8 } = 47 $.	2
4450	$$ a_1 = 46 ~,~ r = 1.003 ~,~ a_n = 14 ~,~ n = ? $$	2