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
5351	$$ a_1 = 9 ~,~ r = 3 ~,~ a_n = 19683 ~,~ n = ? $$	2
5352	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100000 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	2
5353	Find $ a_1 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 5 $.	2
5354	Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	2
5355	$$ a_1 = 1 ~,~ r = 4 ~,~ S_n = 4096 ~,~ n = ? $$	2
5356	Find $ a_1 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 4 $.	2
5357	Find $ a_1 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 8 $.	2
5358	Find $ a_2 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $.	2
5359	Find $ a_2 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = -5 $.	2
5360	Find $ a_5 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = -5 $.	2
5361	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -2 $.	2
5362	Find $ a_2 $ of a geometric progression if $ a_1 = -14 ~~ \text{and} ~~ r = 2 $.	2
5363	Find $ a_3 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	2
5364	Find $ a_3 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $.	2
5365	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 6 $.	2
5366	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 42 ~~ \text{and} ~~ r = 7 $.	2
5367	Find $ a_5 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = -1 $.	2
5368	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 12443 ~~ \text{and} ~~ r = 1.08 $.	2
5369	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.482 $.	2
5370	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.482 $.	2
5371	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.675 $.	2
5372	Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.0325 $.	2
5373	Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.1375 $.	2
5374	Find $ a_2 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -5 $.	2
5375	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
5376	Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	2
5377	$$ a_1 = 9 ~,~ r = 4 ~,~ S_n = 9437184 ~,~ n = ? $$	2
5378	$$ a_1 = 9 ~,~ r = 4 ~,~ a_n = 9437184 ~,~ n = ? $$	2
5379	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.	2
5380	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	2
5381	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	2
5382	Find $ a_1 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $.	2
5383	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = \frac{ 18 }{ 5 } $.	2
5384	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	2
5385	Find $ a_5 $ of a geometric progression if $ a_1 = 24000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 20 } $.	2
5386	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 7 }{ 6 } $.	2
5387	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 8 } = 1640 $.	2
5388	Find $ a_71 $ of a geometric progression if $ a_1 = -52 ~~ \text{and} ~~ r = -13 $.	2
5389	Find $ a_4 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
5390	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 5 ~~ \text{and} ~~ a_{ 2 } = 80 $.	2
5391	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 12 ~~ \text{and} ~~ a_{ 2 } = 10 $.	2
5392	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 25 ~~ \text{and} ~~ a_{ 2 } = 36 $.	2
5393	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 57 }{ 50 } ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2
5394	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
5395	Find $ a_15 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
5396	$$ a_1 = 6 ~,~ r = 2 ~,~ a_n = 20 ~,~ n = ? $$	2
5397	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 150000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5398	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
5399	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = -2 $.	2
5400	Find $ a_3 $ of a geometric progression if $ a_1 = 100000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 100 } $.	2