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
6751	$$ a_1 = 10 ~,~ r = 1.5 ~,~ S_n = 340 ~,~ n = ? $$	1
6752	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
6753	Find $ a_2 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -4 $.	1
6754	Find $ a_2 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 5 $.	1
6755	Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6756	Find $ a_29 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6757	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	1
6758	Find $ a_6 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = -2 $.	1
6759	Find $ a_6 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 2 $.	1
6760	Find $ a_10 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $.	1
6761	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 323 ~~ \text{and} ~~ r = -\frac{ 1 }{ 6 } $.	1
6762	Find $ a_6 $ of a geometric progression if $ a_1 = 0.0124 ~~ \text{and} ~~ r = 100 $.	1
6763	Find $ a_12 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
6764	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
6765	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $.	1
6766	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
6767	Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 4 $.	1
6768	Find $ a_20 $ of a geometric progression if $ a_1 = 6144 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6769	Find $ a_10 $ of a geometric progression if $ a_1 = 6144 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6770	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6144 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
6771	Find the sum of the first $ 46656 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -6 $.	1
6772	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
6773	Find $ a_3 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 4 $.	1
6774	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
6775	Find $ a_5 $ of a geometric progression if $ a_1 = 48 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
6776	Find $ a_5 $ of a geometric progression if $ a_1 = 432 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
6777	Find $ a_5 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
6778	Find $ a_5 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
6779	Find $ a_20 $ of a geometric progression if $ a_1 = 47000 ~~ \text{and} ~~ r = 0.98 $.	1
6780	Find $ a_20 $ of a geometric progression if $ a_1 = 47000 ~~ \text{and} ~~ r = 0.96 $.	1
6781	Find $ a_20 $ of a geometric progression if $ a_1 = 47000 ~~ \text{and} ~~ r = 0.95 $.	1
6782	Find $ a_4 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 5 $.	1
6783	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 6 }{ 5 } ~~ \text{and} ~~ r = 5 $.	1
6784	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
6785	Find $ a_9 $ of a geometric progression if $ a_1 = 63 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
6786	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 3 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
6787	Find $ a_8 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 4 $.	1
6788	Find $ a_9 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 7 } $.	1
6789	$$ a_1 = 1 ~~,~~ r = \frac{ 1 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$	1
6790	Find $ a_7 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6791	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2.003 $.	1
6792	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2.003 $.	1
6793	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2.002 $.	1
6794	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2.001 $.	1
6795	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2.001 $.	1
6796	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 10 $.	1
6797	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = 8 $.	1
6798	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 8 } $.	1
6799	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
6800	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0.0625 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	1