Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 1251 | Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 5 |
| 1252 | Find $ a_6 $ of a geometric progression if $ a_1 = 0.6 ~~ \text{and} ~~ r = -5 $. | 5 |
| 1253 | Find $ a_6 $ of a geometric progression if $ a_1 = 0.1 ~~ \text{and} ~~ r = 0.9 $. | 5 |
| 1254 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -54 ~~ \text{and} ~~ r = -3 $. | 5 |
| 1255 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -1 $. | 5 |
| 1256 | Find $ a_78 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $. | 5 |
| 1257 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $. | 5 |
| 1258 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -6 ~~ \text{and} ~~ r = -\frac{ 2 }{ 5 } $. | 5 |
| 1259 | Find the sum of the first $ 999999 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.1416 $. | 5 |
| 1260 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1261 | Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 5 |
| 1262 | $$ a_1 = 9600 ~,~ r = \frac{ 6 }{ 5 } ~,~ a_n = 18 ~,~ n = ? $$ | 5 |
| 1263 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 5 |
| 1264 | $$ a_1 = 10 ~~,~~ r = -3 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 5 |
| 1265 | Find the sum of the first $ 194 $ terms of a geometric sequence if $ a_1 = 229 ~~ \text{and} ~~ r = 1 $. | 5 |
| 1266 | Find $ a_15 $ of a geometric progression if $ a_1 = 6144 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 5 |
| 1267 | Find $ a_1 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 5 } $. | 5 |
| 1268 | $$ a_1 = 25000 ~~,~~ r = \frac{ 9 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 5 |
| 1269 | Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $. | 5 |
| 1270 | Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -4 $. | 5 |
| 1271 | Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 5 |
| 1272 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 0.333 $. | 5 |
| 1273 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 121 ~~ \text{and} ~~ r = 0.016 $. | 5 |
| 1274 | Find $ a_34 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.108 $. | 5 |
| 1275 | Find $ a_34 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.118 $. | 5 |
| 1276 | Find $ a_34 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.122 $. | 5 |
| 1277 | Find $ a_34 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.133 $. | 5 |
| 1278 | Find $ a_39 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.128 $. | 5 |
| 1279 | Find $ a_5 $ of a geometric progression if $ a_1 = 1000000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 5 |
| 1280 | Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $. | 5 |
| 1281 | Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 0.93 ~~ \text{and} ~~ r = 2.25 $. | 5 |
| 1282 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = 0.1 $. | 5 |
| 1283 | Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1284 | Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $. | 5 |
| 1285 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 6 $. | 5 |
| 1286 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $. | 5 |
| 1287 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $. | 5 |
| 1288 | Find $ a_14 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $. | 5 |
| 1289 | Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 5 |
| 1290 | Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 5 |
| 1291 | Find $ a_8 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 5 |
| 1292 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = -1.67 $. | 5 |
| 1293 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 5 |
| 1294 | Find $ a_200 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 200 $. | 5 |
| 1295 | Find $ a_150 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 150 $. | 5 |
| 1296 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $. | 5 |
| 1297 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 10 $. | 5 |
| 1298 | $$ a_1 = 130000 ~,~ r = \frac{ 97 }{ 100 } ~,~ a_n = 14 ~,~ n = ? $$ | 5 |
| 1299 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 5 |
| 1300 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 5 |
