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
2751	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $.	3
2752	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $.	3
2753	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $.	3
2754	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 35000 ~~ \text{and} ~~ r = 0.025 $.	3
2755	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	3
2756	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 12 $.	3
2757	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 25000 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	3
2758	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	3
2759	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	3
2760	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 162 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	3
2761	Find $ a_11 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	3
2762	Find $ a_11 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	3
2763	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $.	3
2764	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	3
2765	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	3
2766	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	3
2767	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 6 $.	3
2768	$$ a_1 = 4 ~~,~~ r = -4 ~~,~~ a_1 = ? ~~,~~ r = ? $$	3
2769	Find $ a_8 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = 1 $.	3
2770	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	3
2771	Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2772	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.367 $.	3
2773	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 0.5 $.	3
2774	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 3 $.	3
2775	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 256 } ~~ \text{and} ~~ r = 4 $.	3
2776	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	3
2777	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2778	Find $ a_4 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 10 $.	3
2779	$$ a_1 = 2 ~,~ r = 5 ~,~ S_n = 3 ~,~ n = ? $$	3
2780	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.1 $.	3
2781	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	3
2782	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	3
2783	Find $ a_8 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -2 $.	3
2784	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2785	Find $ a_25 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 2 $.	3
2786	Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	3
2787	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 2.9 ~~ \text{and} ~~ r = 1.3 $.	3
2788	Find $ a_6 $ of a geometric progression if $ a_1 = -12 ~~ \text{and} ~~ r = 4 $.	3
2789	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	3
2790	Find $ a_6 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2791	Find $ a_10 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = -3 $.	3
2792	Find $ a_7 $ of a geometric progression if $ a_1 = 10800 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	3
2793	Find $ a_10 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 3 $.	3
2794	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2795	Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2796	Find $ a_512 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = 64 $.	3
2797	Find $ a_11 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	3
2798	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.	3
2799	Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	3
2800	Find $ a_6 $ of a geometric progression if $ a_1 = 224 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3