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
1301	Find $ a_30 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	5
1302	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 4569 }{ 25 } ~~ \text{and} ~~ r = 1.048 $.	5
1303	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 109659 }{ 50 } ~~ \text{and} ~~ r = 1.048 $.	5
1304	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 0.06 ~~ \text{and} ~~ r = 1.3 $.	5
1305	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	5
1306	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -64 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	5
1307	Find $ a_35 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	5
1308	Find $ a_6 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1309	Find $ a_9 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -9 $.	5
1310	Find $ a_8 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 7 $.	5
1311	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = 2 $.	5
1312	Find $ a_6 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1313	Find $ a_10 $ of a geometric progression if $ a_1 = 43 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	5
1314	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 250 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	5
1315	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 24 } ~~ \text{and} ~~ r = -2 $.	5
1316	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -2 $.	5
1317	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	5
1318	Find $ a_3 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	5
1319	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 1 $.	5
1320	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 7 $.	5
1321	Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -5 $.	5
1322	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	5
1323	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2.5 $.	5
1324	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	5
1325	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 360 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $.	5
1326	Find $ a_8 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	5
1327	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 0.0001 ~~ \text{and} ~~ r = 1.25 $.	5
1328	Find $ a_7 $ of a geometric progression if $ a_1 = -27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1329	Find $ a_4 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1330	Find $ a_5 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1331	Find $ a_6 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1332	Find $ a_7 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1333	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $.	5
1334	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $.	5
1335	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	5
1336	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	5
1337	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $.	5
1338	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = 4 $.	5
1339	Find $ a_11 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	5
1340	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	5
1341	Find $ a_7 $ of a geometric progression if $ a_1 = 120 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	5
1342	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1343	Find $ a_52 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 1.1 $.	5
1344	Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	5
1345	Find $ a_3 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	5
1346	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	5
1347	Find $ a_3 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	5
1348	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	5
1349	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	5
1350	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1324 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5