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
10801	Find $ a_1000000 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -0.75 $.	1
10802	Find $ a_1000000 $ of a geometric progression if $ a_1 = -0.75 ~~ \text{and} ~~ r = 5 $.	1
10803	Find $ a_8 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
10804	Find $ a_8 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
10805	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	1
10806	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10807	Find $ a_18 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	1
10808	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -8 $.	1
10809	Find $ a_5 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 2 $.	1
10810	$$ a_1 = 1000 ~,~ r = \frac{ 91 }{ 100 } ~,~ a_n = 500 ~,~ n = ? $$	1
10811	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -200 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10812	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
10813	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -6 $.	1
10814	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 6 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 8 }{ 5 } $.	1
10815	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10816	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	1
10817	$$ a_1 = -3 ~~,~~ r = -4 ~~,~~ a_1 = ? ~~,~~ r = ? $$	1
10818	Find $ a_12 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
10819	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = 5 $.	1
10820	Find $ a_10 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = 2 $.	1
10821	Find $ a_10 $ of a geometric progression if $ a_1 = -32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
10822	Find $ a_9 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	1
10823	Find $ a_10 $ of a geometric progression if $ a_1 = 7300000000 ~~ \text{and} ~~ r = 0.0167 $.	1
10824	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 35 ~~ \text{and} ~~ r = -2 $.	1
10825	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $.	1
10826	Find $ a_7 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 17 }{ 20 } $.	1
10827	Find $ a_3 $ of a geometric progression if $ a_1 = 1472 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
10828	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 18 }{ 11 } $.	1
10829	Find $ a_5 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = 7 $.	1
10830	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10831	Find $ a_14 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.	1
10832	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	1
10833	Find $ a_4 $ of a geometric progression if $ a_1 = 99 ~~ \text{and} ~~ r = 2 $.	1
10834	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 1 }{ 8 } ~~ \text{and} ~~ a_{ 5 } = 1 $.	1
10835	Find $ a_7 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
10836	Find $ a_4 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = -5 $.	1
10837	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 8 } ~~ \text{and} ~~ r = -\frac{ 8 }{ 9 } $.	1
10838	Find the sum of the first $ 100000000 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = 0.8 $.	1
10839	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = 0.8 $.	1
10840	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 6 $.	1
10841	Find $ a_7 $ of a geometric progression if $ a_1 = -8.54 ~~ \text{and} ~~ r = -8.54 $.	1
10842	Find $ a_5 $ of a geometric progression if $ a_1 = -\dfrac{ 21 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.	1
10843	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 34 $.	1
10844	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $.	1
10845	$$ a_1 = 1 ~,~ r = 10 ~,~ S_n = 70000 ~,~ n = ? $$	1
10846	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.	1
10847	Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 7 } ~~ \text{and} ~~ r = 3 $.	1
10848	Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 0.0006667 $.	1
10849	Find the sum of the first $ 999999 $ terms of a geometric sequence if $ a_1 = 0.9 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
10850	Find the sum of the first $ 99 $ terms of a geometric sequence if $ a_1 = \frac{ 9 }{ 10 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1