Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
10551	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10552	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
10553	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10554	Find $ a_7 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = 2 $.	1
10555	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 170 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
10556	Find $ a_7 $ of a geometric progression if $ a_1 = -\dfrac{ 8 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	1
10557	Find $ a_7 $ of a geometric progression if $ a_1 = -\dfrac{ 8 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10558	Find $ a_1000 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	1
10559	Find $ a_138149 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 0.9999 $.	1
10560	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 4000 ~~ \text{and} ~~ r = 1.3 $.	1
10561	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 187345 ~~ \text{and} ~~ r = \frac{ 1 }{ 50 } $.	1
10562	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 3 $.	1
10563	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 3 $.	1
10564	$$ a_1 = \frac{ 1 }{ 4 } ~,~ r = 3 ~,~ a_n = 10 ~,~ n = ? $$	1
10565	Find $ a_3 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 20 $.	1
10566	Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $.	1
10567	$$ a_1 = 2 ~,~ r = 3 ~,~ a_n = 1458 ~,~ n = ? $$	1
10568	Find $ a_2 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10569	Find $ a_6 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10570	Find $ a_12 $ of a geometric progression if $ a_1 = 216 ~~ \text{and} ~~ r = 0.1667 $.	1
10571	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 216 ~~ \text{and} ~~ r = 0.1667 $.	1
10572	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 4 $.	1
10573	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -2 $.	1
10574	Find $ a_2 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
10575	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ r = 2 $.	1
10576	Find $ a_50 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -1 $.	1
10577	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	1
10578	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 1 $.	1
10579	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	1
10580	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 120 ~~ \text{and} ~~ a_{ 5 } = 160 $.	1
10581	Find $ a_10 $ of a geometric progression if $ a_1 = 1250 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
10582	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	1
10583	Find the sum of the first $ 150 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 0.1 $.	1
10584	Find $ a_100 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	1
10585	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 3 $.	1
10586	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1.08 ~~ \text{and} ~~ r = 1.08 $.	1
10587	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	1
10588	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 5 }{ 3 } $.	1
10589	Find $ a_11 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 2 $.	1
10590	Find the sum of the first $ 10000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 7 }{ 12 } $.	1
10591	Find $ a_2 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -4 $.	1
10592	Find $ a_8 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	1
10593	Find $ a_20 $ of a geometric progression if $ a_1 = 1692 ~~ \text{and} ~~ r = 2 $.	1
10594	Find $ a_121 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.1 $.	1
10595	Find $ a_11 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.1 $.	1
10596	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 5730 ~~ \text{and} ~~ r = 0.5 $.	1
10597	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5730 ~~ \text{and} ~~ r = 0.5 $.	1
10598	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	1
10599	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
10600	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 10 $.	1