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
9101	Find $ a_3 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	1
9102	Find $ a_5 $ of a geometric progression if $ a_1 = -375 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9103	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 23000 ~~ \text{and} ~~ r = \frac{ 103 }{ 100 } $.	1
9104	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
9105	Find $ a_1 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9106	Find $ a_11 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
9107	Find $ a_13 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 3 $.	1
9108	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 16 ~~ \text{and} ~~ a_{ 5 } = \frac{ 7503 }{ 50 } $.	1
9109	Find $ a_17 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 1.75 $.	1
9110	Find $ a_5 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = 3 $.	1
9111	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 6 } $.	1
9112	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 256 } ~~ \text{and} ~~ r = 4 $.	1
9113	$$ a_1 = 6 ~,~ r = 8 ~,~ a_n = 805306368 ~,~ n = ? $$	1
9114	$$ a_1 = 1000 ~,~ r = 0.9 ~,~ a_n = 1.0E-7 ~,~ n = ? $$	1
9115	Find $ a_5 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9116	Find the sum of the first $ 99 $ terms of a geometric sequence if $ a_1 = 90 ~~ \text{and} ~~ r = 1.04 $.	1
9117	Find the sum of the first $ 99 $ terms of a geometric sequence if $ a_1 = 90 ~~ \text{and} ~~ r = 1.03 $.	1
9118	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 270 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
9119	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = 20 $.	1
9120	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 150 ~~ \text{and} ~~ r = 1.02 $.	1
9121	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
9122	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = -0.03125 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
9123	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -0.03125 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
9124	Find $ a_9 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9125	Find $ a_7 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9126	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9127	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = 5 $.	1
9128	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	1
9129	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
9130	Find $ a_7 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9131	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 24 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9132	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9133	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	1
9134	Find $ a_3 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.	1
9135	Find $ a_5 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = 11 $.	1
9136	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $.	1
9137	Find $ a_10 $ of a geometric progression if $ a_1 = 1600 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $.	1
9138	Find $ a_10 $ of a geometric progression if $ a_1 = 1600 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9139	Find $ a_10 $ of a geometric progression if $ a_1 = 1600 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $.	1
9140	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 9 } $.	1
9141	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	1
9142	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9143	Find $ a_40 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 6 $.	1
9144	Find $ a_6 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -4 $.	1
9145	Find $ a_6 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $.	1
9146	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -2 $.	1
9147	Find $ a_20 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9148	$$ a_1 = 78732 ~,~ r = \frac{ 1 }{ 3 } ~,~ S_n = 11896 ~,~ n = ? $$	1
9149	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	1
9150	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 100 } $.	1