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
10101	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 10 $.	1
10102	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10103	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = 3 $.	1
10104	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $.	1
10105	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
10106	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	1
10107	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.367 $.	1
10108	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.367 $.	1
10109	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
10110	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10111	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 16 } ~~ \text{and} ~~ r = 4 $.	1
10112	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 9 } ~~ \text{and} ~~ r = -6 $.	1
10113	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = -5 $.	1
10114	Find the sum of the first $ 10000000000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.75 $.	1
10115	Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.75 $.	1
10116	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.75 $.	1
10117	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	1
10118	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	1
10119	Find $ a_10 $ of a geometric progression if $ a_1 = 1258 ~~ \text{and} ~~ r = 5.1 $.	1
10120	Find $ a_9 $ of a geometric progression if $ a_1 = -65538 ~~ \text{and} ~~ r = -0.25 $.	1
10121	Find $ a_7 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 4 $.	1
10122	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 125 } ~~ \text{and} ~~ r = 5 $.	1
10123	Find $ a_6 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 6 $.	1
10124	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10125	Find $ a_4 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	1
10126	$$ a_1 = 4 ~,~ r = 2 ~,~ a_n = 8 ~,~ n = ? $$	1
10127	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $.	1
10128	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 625 } ~~ \text{and} ~~ r = 5 $.	1
10129	Find $ a_7 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = 2 $.	1
10130	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10131	Find $ a_4 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	1
10132	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
10133	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	1
10134	Find $ a_16 $ of a geometric progression if $ a_1 = 900 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10135	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	1
10136	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	1
10137	Find $ a_15 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 9 } ~~ \text{and} ~~ r = 2 $.	1
10138	Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	1
10139	Find $ a_13 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 3 $.	1
10140	Find $ a_2 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	1
10141	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = -\frac{ 5 }{ 6 } $.	1
10142	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 64 } ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	1
10143	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 64 } ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	1
10144	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 11 } $.	1
10145	Find the sum of the first $ 1500 $ terms of a geometric sequence if $ a_1 = \frac{ 49 }{ 10 } ~~ \text{and} ~~ r = 0.06425 $.	1
10146	Find the sum of the first $ 1500 $ terms of a geometric sequence if $ a_1 = \frac{ 49 }{ 10 } ~~ \text{and} ~~ r = 0.9358 $.	1
10147	Find the sum of the first $ 1500 $ terms of a geometric sequence if $ a_1 = \frac{ 49 }{ 10 } ~~ \text{and} ~~ r = 0.995 $.	1
10148	Find the sum of the first $ 1500 $ terms of a geometric sequence if $ a_1 = \frac{ 49 }{ 10 } ~~ \text{and} ~~ r = 0.9973 $.	1
10149	Find the sum of the first $ 1500 $ terms of a geometric sequence if $ a_1 = \frac{ 49 }{ 10 } ~~ \text{and} ~~ r = 0.9989 $.	1
10150	Find $ a_20 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1