Geometric sequences

(the database of solved problems)

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

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ID	Problem	Count
2701	Find $ a_10 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	3
2702	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.0001 ~~ \text{and} ~~ r = 1.25 $.	3
2703	Find $ a_9 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2704	Find $ a_4 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	3
2705	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	3
2706	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	3
2707	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	3
2708	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	3
2709	Find $ a_10 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2710	Find $ a_14 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	3
2711	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 8 $.	3
2712	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = -3 $.	3
2713	Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 7 $.	3
2714	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 6 $.	3
2715	Find $ a_6 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	3
2716	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	3
2717	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	3
2718	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 3 $.	3
2719	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 5 } ~~ \text{and} ~~ r = -5 $.	3
2720	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	3
2721	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	3
2722	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	3
2723	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	3
2724	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	3
2725	Find $ a_8 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 9 } $.	3
2726	Find $ a_8 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2727	Find $ a_6 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	3
2728	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 45 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	3
2729	Find $ a_14 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	3
2730	Find $ a_8 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -3 $.	3
2731	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = 2 $.	3
2732	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1988 ~~ \text{and} ~~ r = 0.85 $.	3
2733	Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 11 } $.	3
2734	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $.	3
2735	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	3
2736	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	3
2737	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 24 ~~ \text{and} ~~ r = -2 $.	3
2738	Find $ a_7 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 2 $.	3
2739	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2740	Find $ a_10 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 4 $.	3
2741	Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	3
2742	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = -5 $.	3
2743	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	3
2744	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 35 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	3
2745	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 8 }{ 5 } ~~ \text{and} ~~ a_{ 7 } = 2080 $.	3
2746	Find $ a_15 $ of a geometric progression if $ a_1 = -2187 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	3
2747	Find $ a_15 $ of a geometric progression if $ a_1 = -2187 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	3
2748	Find $ a_10 $ of a geometric progression if $ a_1 = 100000 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	3
2749	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 27 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	3
2750	Find $ a_11 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 6 $.	3