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
10501	Find $ a_12 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.	1
10502	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	1
10503	Find $ a_7 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
10504	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	1
10505	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 100 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	1
10506	Find $ a_12 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 2 $.	1
10507	Find $ a_11 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
10508	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
10509	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 2 $.	1
10510	Find $ a_20 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10511	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = 0.3333 $.	1
10512	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = 2 $.	1
10513	Find $ a_6 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 2 $.	1
10514	Find $ a_12 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 2 $.	1
10515	Find $ a_8 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 2 $.	1
10516	Find the sum of the first $ 9999999999 $ terms of a geometric sequence if $ a_1 = 0.9 ~~ \text{and} ~~ r = 0.1 $.	1
10517	Find $ a_4 $ of a geometric progression if $ a_1 = 620 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.	1
10518	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	1
10519	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 5 ~~ \text{and} ~~ a_{ 3 } = 17 $.	1
10520	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
10521	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
10522	Find $ a_10 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 1.025 $.	1
10523	Find $ a_10 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.025 $.	1
10524	Find $ a_6 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 2 } $.	1
10525	Find $ a_3 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	1
10526	Find $ a_20 $ of a geometric progression if $ a_1 = 1500 ~~ \text{and} ~~ r = 1.5 $.	1
10527	Find $ a_17 $ of a geometric progression if $ a_1 = 2600 ~~ \text{and} ~~ r = 1.4 $.	1
10528	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $.	1
10529	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 5700 ~~ \text{and} ~~ r = 1.1 $.	1
10530	Find $ a_15 $ of a geometric progression if $ a_1 = 18000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
10531	Find $ a_13 $ of a geometric progression if $ a_1 = 18000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
10532	Find $ a_14 $ of a geometric progression if $ a_1 = 18000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
10533	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.0005 ~~ \text{and} ~~ r = 1.2 $.	1
10534	Find $ a_7 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 2 } $.	1
10535	Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	1
10536	Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
10537	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	1
10538	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
10539	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 22000 ~~ \text{and} ~~ a_{ 2 } = 22500 $.	1
10540	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 50 ~~ \text{and} ~~ a_{ 6 } = 750 $.	1
10541	$$ a_1 = 2 ~,~ r = 2 ~,~ a_n = 9 ~,~ n = ? $$	1
10542	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10543	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = -\frac{ 8 }{ 9 } $.	1
10544	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = -2 $.	1
10545	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	1
10546	Find $ a_7 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 2 $.	1
10547	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -1 $.	1
10548	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = -1 $.	1
10549	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
10550	Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1