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
2551	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	3
2552	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	3
2553	Find the sum of the first $ 365 $ terms of a geometric sequence if $ a_1 = 0.01 ~~ \text{and} ~~ r = 2 $.	3
2554	Find the sum of the first $ 55 $ terms of a geometric sequence if $ a_1 = 22 ~~ \text{and} ~~ r = 33 $.	3
2555	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	3
2556	Find $ a_10 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $.	3
2557	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 5 } $.	3
2558	Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	3
2559	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	3
2560	Find $ a_7 $ of a geometric progression if $ a_1 = 50500 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	3
2561	Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2562	Find $ a_11 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	3
2563	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 8 } $.	3
2564	Find $ a_8 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	3
2565	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	3
2566	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2567	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.025 $.	3
2568	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 3 $.	3
2569	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	3
2570	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	3
2571	Find $ a_6 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2572	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	3
2573	Find $ a_8 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	3
2574	Find $ a_6 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2575	Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $.	3
2576	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 1 }{ 8 } $.	3
2577	Find $ a_10 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	3
2578	Find $ a_10 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 2 $.	3
2579	Find $ a_50 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 2 $.	3
2580	Find $ a_7 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2581	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	3
2582	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.33 $.	3
2583	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	3
2584	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2585	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1024 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2586	Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	3
2587	Find $ a_1 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	3
2588	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	3
2589	Find $ a_1 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	3
2590	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 4 $.	3
2591	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -2 $.	3
2592	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	3
2593	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1200 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	3
2594	Find $ a_16 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	3
2595	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2596	Find $ a_1 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	3
2597	Find $ a_6 $ of a geometric progression if $ a_1 = 15624 ~~ \text{and} ~~ r = 5 $.	3
2598	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	3
2599	$$ a_1 = 5 ~,~ r = 4 ~,~ S_n = 105 ~,~ n = ? $$	3
2600	Find $ a_11 $ of a geometric progression if $ a_1 = 39000 ~~ \text{and} ~~ r = 0.05 $.	3