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
7401	Find $ a_10 $ of a geometric progression if $ a_1 = -\dfrac{ 4 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
7402	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	1
7403	Find $ a_3 $ of a geometric progression if $ a_1 = 91800 ~~ \text{and} ~~ r = \dfrac{ 103 }{ 100 } $.	1
7404	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 512 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
7405	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 512 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
7406	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	1
7407	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = 8 ~~ \text{and} ~~ a_{ 7 } = \frac{ 64 }{ 27 } $.	1
7408	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
7409	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = 2 $.	1
7410	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 15 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
7411	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 15 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
7412	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = \frac{ 15 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
7413	Find $ a_9 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
7414	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
7415	Find $ a_2 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 101 }{ 100 } $.	1
7416	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 101 }{ 100 } $.	1
7417	Find the sum of the first $ 24 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 1.01 $.	1
7418	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -100 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
7419	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
7420	Find $ a_15 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
7421	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 49 }{ 9 } $.	1
7422	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
7423	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.	1
7424	$$ a_1 = 15 ~,~ r = 2 ~,~ a_n = 500 ~,~ n = ? $$	1
7425	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
7426	$$ a_1 = 1 ~,~ r = 5 ~,~ S_n = 156 ~,~ n = ? $$	1
7427	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 4.625 ~~ \text{and} ~~ a_{ 6 } = 6.576 $.	1
7428	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	1
7429	Find $ a_11 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -3 $.	1
7430	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2700 ~~ \text{and} ~~ r = 10 $.	1
7431	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
7432	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
7433	Find $ a_1 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 2 $.	1
7434	Find $ a_9 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -1 $.	1
7435	Find $ a_9 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -2 $.	1
7436	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	1
7437	Find $ a_28 $ of a geometric progression if $ a_1 = 8500 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
7438	Find $ a_3840 $ of a geometric progression if $ a_1 = 6.5 ~~ \text{and} ~~ r = 1.02 $.	1
7439	Find the sum of the first $ 3840 $ terms of a geometric sequence if $ a_1 = 6.5 ~~ \text{and} ~~ r = 1.02 $.	1
7440	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6.5 ~~ \text{and} ~~ r = 1.02 $.	1
7441	Find $ a_8 $ of a geometric progression if $ a_1 = 6.5 ~~ \text{and} ~~ r = 1.02 $.	1
7442	Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
7443	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	1
7444	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
7445	Find $ a_9 $ of a geometric progression if $ a_1 = 19 ~~ \text{and} ~~ r = 3 $.	1
7446	Find $ a_12 $ of a geometric progression if $ a_1 = -20 ~~ \text{and} ~~ r = -1 $.	1
7447	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
7448	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	1
7449	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 9 } ~~ \text{and} ~~ r = 3 $.	1
7450	Find $ a_4 $ of a geometric progression if $ a_1 = 2187 ~~ \text{and} ~~ r = 27 $.	1