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
2401	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	4
2402	Find the sum of the first $ 2048 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	4
2403	Find $ a_8 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	4
2404	Find $ a_4 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	4
2405	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 6 ~~ \text{and} ~~ a_{ 7 } = -113 $.	3
2406	Find $ a_5 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2407	Find $ a_5 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2408	Find $ a_3 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -4 $.	3
2409	Find $ a_7 $ of a geometric progression if $ a_1 = 0.0017 ~~ \text{and} ~~ r = -10 $.	3
2410	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	3
2411	$$ a_1 = \frac{ 9 }{ 8 } ~,~ r = \frac{ 1 }{ 3 } ~,~ a_n = 5 ~,~ n = ? $$	3
2412	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 45 ~~ \text{and} ~~ a_{ 8 } = 360 $.	3
2413	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	3
2414	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	3
2415	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	3
2416	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	3
2417	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = 0.8 $.	3
2418	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2419	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2420	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -6 $.	3
2421	Find $ a_5 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 4 $.	3
2422	Find $ a_9 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = -2 $.	3
2423	Find $ a_6 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	3
2424	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 6 $.	3
2425	Find $ a_10 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	3
2426	Find $ a_7 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = 5 $.	3
2427	Find $ a_10 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	3
2428	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	3
2429	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2430	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	3
2431	Find $ a_8 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 10 $.	3
2432	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 0.125 $.	3
2433	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 8 } $.	3
2434	Find $ a_7 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
2435	Find $ a_3 $ of a geometric progression if $ a_1 = 648 ~~ \text{and} ~~ r = \dfrac{ 10 }{ 9 } $.	3
2436	Find $ a_1 $ of a geometric progression if $ a_1 = -28 ~~ \text{and} ~~ r = 0.4643 $.	3
2437	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	3
2438	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
2439	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2440	Find $ a_8 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
2441	Find $ a_14 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	3
2442	Find $ a_6 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	3
2443	Find $ a_8 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 4 $.	3
2444	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $.	3
2445	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 24000 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	3
2446	Find the sum of the first $ 22 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = 1.025 $.	3
2447	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $.	3
2448	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 13.5 ~~ \text{and} ~~ r = 1.5 $.	3
2449	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 13.5 ~~ \text{and} ~~ r = 1.5 $.	3
2450	Find $ a_15 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 10 $.	3