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
6401	Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
6402	Find $ a_20 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
6403	Find $ a_15 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	2
6404	Find $ a_15 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	2
6405	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	2
6406	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2401 } ~~ \text{and} ~~ r = 1 $.	2
6407	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	2
6408	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	2
6409	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 16807 }{ 32768 } ~~ \text{and} ~~ r = \frac{ 7 }{ 8 } $.	2
6410	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	2
6411	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 125 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
6412	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 125 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	2
6413	Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
6414	Find $ a_21 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
6415	Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
6416	Find $ a_4 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 5 } $.	2
6417	Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
6418	Find $ a_6 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	2
6419	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	2
6420	$$ a_1 = 32 ~,~ r = 32 ~,~ a_n = 1000000 ~,~ n = ? $$	2
6421	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $.	2
6422	Find $ a_15 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6423	Find $ a_11 $ of a geometric progression if $ a_1 = 120000000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
6424	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6425	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 0.02 ~~ \text{and} ~~ r = 2 $.	2
6426	$$ a_1 = 2 ~~,~~ r = 3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
6427	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.	2
6428	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6429	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 6 $.	2
6430	Find $ a_15 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 6 $.	2
6431	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	2
6432	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
6433	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 64 } ~~ \text{and} ~~ r = 4 $.	2
6434	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 729 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
6435	Find $ a_10 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
6436	Find $ a_7 $ of a geometric progression if $ a_1 = -4800 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	2
6437	$$ a_1 = 90 ~~,~~ r = 0.03 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
6438	Find $ a_2 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = 4 $.	2
6439	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	2
6440	Find $ a_3 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 3 $.	2
6441	Find $ a_6 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -5 $.	2
6442	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	2
6443	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = -5 $.	2
6444	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 7 } $.	2
6445	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 4 } ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 5 } $.	2
6446	Find $ a_6 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	2
6447	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 640 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6448	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
6449	Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
6450	Find the sum of the first $ 100000 $ terms of a geometric sequence if $ a_1 = -10 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2