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
1151	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -4 $.	5
1152	Find $ a_5 $ of a geometric progression if $ a_1 = 576 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	5
1153	Find $ a_6 $ of a geometric progression if $ a_1 = 16807 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 7 } $.	5
1154	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	5
1155	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 20 } ~~ \text{and} ~~ r = \dfrac{ 17 }{ 20 } $.	5
1156	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 20 } ~~ \text{and} ~~ r = \frac{ 17 }{ 20 } $.	5
1157	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 20 } ~~ \text{and} ~~ r = \frac{ 17 }{ 20 } $.	5
1158	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 0.15 ~~ \text{and} ~~ r = 0.85 $.	5
1159	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 9 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	5
1160	Find $ a_10 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 3 $.	5
1161	Find $ a_67 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	5
1162	Find $ a_4 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -6 $.	5
1163	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	5
1164	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = 3 $.	5
1165	Find $ a_19 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -4 $.	5
1166	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1167	Find $ a_7 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.	5
1168	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 250 } ~~ \text{and} ~~ r = 5 $.	5
1169	Find the sum of the first $ 27 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -1 $.	5
1170	Find $ a_1 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	5
1171	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $.	5
1172	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1173	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 27 }{ 16 } ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	5
1174	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -2 $.	5
1175	Find $ a_6 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -12 $.	5
1176	Find $ a_5 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 4 $.	5
1177	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	5
1178	Find $ a_9 $ of a geometric progression if $ a_1 = 1875 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	5
1179	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	5
1180	Find $ a_13 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -3 $.	5
1181	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 25000 ~~ \text{and} ~~ r = 1250 $.	5
1182	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 1 $.	5
1183	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	5
1184	$$ a_1 = 24 ~,~ r = 4 ~,~ a_n = 3 ~,~ n = ? $$	5
1185	Find $ a_15 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	5
1186	Find $ a_16 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	5
1187	Find $ a_9 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	5
1188	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	5
1189	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	5
1190	Find $ a_12 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	5
1191	Find $ a_10 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	5
1192	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	5
1193	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = 2 $.	5
1194	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	5
1195	Find $ a_7 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 20 } $.	5
1196	Find $ a_10 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = -2 $.	5
1197	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = 3 $.	5
1198	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 3 $.	5
1199	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	5
1200	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 512 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	5