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
1101	Find $ a_83 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 1.01 $.	5
1102	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	5
1103	Find $ a_12 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	5
1104	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 6 $.	5
1105	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 10 } ~~ \text{and} ~~ r = 9 $.	5
1106	Find $ a_8 $ of a geometric progression if $ a_1 = 432 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	5
1107	Find $ a_8 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	5
1108	Find $ a_3 $ of a geometric progression if $ a_1 = 77 ~~ \text{and} ~~ r = 2.93 $.	5
1109	Find $ a_3 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 2.93 $.	5
1110	$$ a_1 = 25 ~,~ r = \frac{ 77 }{ 25 } ~,~ a_n = 4 ~,~ n = ? $$	5
1111	$$ a_1 = 25 ~,~ r = 3.08 ~,~ a_n = 4 ~,~ n = ? $$	5
1112	$$ a_1 = 226 ~,~ r = 3.01 ~,~ a_n = 4 ~,~ n = ? $$	5
1113	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 25 ~~ \text{and} ~~ r = 3.006 $.	5
1114	Find $ a_5 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 3.006 $.	5
1115	Find $ a_3 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	5
1116	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	5
1117	Find $ a_9 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1118	Find $ a_5 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 20 } $.	5
1119	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	5
1120	Find $ a_100 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1121	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -729 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	5
1122	Find $ a_5 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	5
1123	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 2 $.	5
1124	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 25 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	5
1125	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1280 }{ 567 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	5
1126	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $.	5
1127	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = 1 $.	5
1128	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = -3 $.	5
1129	Find $ a_31 $ of a geometric progression if $ a_1 = 67900 ~~ \text{and} ~~ r = 0.943 $.	5
1130	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -\frac{ 4 }{ 5 } ~~ \text{and} ~~ r = -5 $.	5
1131	Find $ a_12 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = 8 $.	5
1132	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1133	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	5
1134	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	5
1135	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 21 } $.	5
1136	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 2 $.	5
1137	Find $ a_7 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	5
1138	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	5
1139	Find $ a_8 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -3 $.	5
1140	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $.	5
1141	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -\frac{ 4 }{ 5 } ~~ \text{and} ~~ r = -\frac{ 4 }{ 5 } $.	5
1142	Find $ a_11 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	5
1143	Find $ a_7 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -2 $.	5
1144	Find $ a_9 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1145	Find $ a_3 $ of a geometric progression if $ a_1 = 240 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	5
1146	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -4 $.	5
1147	Find $ a_5 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1148	Find $ a_9 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1149	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 10 $.	5
1150	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	5