Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 1401 | Find $ a_23 $ of a geometric progression if $ a_1 = 15000 ~~ \text{and} ~~ r = 1.1 $. | 5 |
| 1402 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 6 $. | 5 |
| 1403 | Find $ a_9 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 5 |
| 1404 | Find $ a_5 $ of a geometric progression if $ a_1 = 700000 ~~ \text{and} ~~ r = \dfrac{ 17 }{ 20 } $. | 5 |
| 1405 | Find $ a_12 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 0.9 $. | 5 |
| 1406 | Find $ a_6 $ of a geometric progression if $ a_1 = 850 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $. | 5 |
| 1407 | Find $ a_20 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $. | 5 |
| 1408 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 5 |
| 1409 | Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $. | 5 |
| 1410 | Find the sum of the first $ 24 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $. | 5 |
| 1411 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 5 |
| 1412 | $$ a_1 = 1 ~,~ r = 2 ~,~ a_n = 37 ~,~ n = ? $$ | 5 |
| 1413 | $$ a_1 = \frac{ 1 }{ 7 } ~,~ r = 3 ~,~ a_n = \frac{ 6561 }{ 7 } ~,~ n = ? $$ | 5 |
| 1414 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1530 ~~ \text{and} ~~ r = \frac{ 23 }{ 20 } $. | 5 |
| 1415 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 6 } ~~ \text{and} ~~ r = 3 $. | 5 |
| 1416 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 300000 ~~ \text{and} ~~ r = 1.082 $. | 5 |
| 1417 | Find $ a_12 $ of a geometric progression if $ a_1 = 250 ~~ \text{and} ~~ r = 0.1 $. | 5 |
| 1418 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 5 |
| 1419 | Find $ a_4 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 5 |
| 1420 | Find $ a_5 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 5 |
| 1421 | Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 100 } ~~ \text{and} ~~ r = 2 $. | 5 |
| 1422 | Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 0.968 ~~ \text{and} ~~ r = 0.968 $. | 5 |
| 1423 | Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 0.9972 ~~ \text{and} ~~ r = 0.9972 $. | 5 |
| 1424 | Find $ a_3 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 5 |
| 1425 | Find $ a_4 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 5 |
| 1426 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $. | 5 |
| 1427 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $. | 5 |
| 1428 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $. | 5 |
| 1429 | $$ a_1 = 1 ~,~ r = 2 ~,~ S_n = 1000000 ~,~ n = ? $$ | 5 |
| 1430 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 7 }{ 12 } ~~ \text{and} ~~ r = \frac{ 49 }{ 9 } $. | 5 |
| 1431 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $. | 5 |
| 1432 | Find $ a_11 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $. | 5 |
| 1433 | Find $ a_4 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -4 $. | 5 |
| 1434 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = 3 $. | 5 |
| 1435 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $. | 5 |
| 1436 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 5 |
| 1437 | Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 24 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $. | 5 |
| 1438 | Find $ a_6 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 5 $. | 5 |
| 1439 | Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 5 |
| 1440 | Find $ a_2 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 3 $. | 5 |
| 1441 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 4 } = \frac{ 4 }{ 3 } ~~ \text{and} ~~ a_{ 7 } = \frac{ 64 }{ 243 } $. | 5 |
| 1442 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 7 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 5 |
| 1443 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = -2 $. | 5 |
| 1444 | Find $ a_11 $ of a geometric progression if $ a_1 = 3.75 ~~ \text{and} ~~ r = 6.923 $. | 5 |
| 1445 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1875 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 5 |
| 1446 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1875 ~~ \text{and} ~~ r = 0.2 $. | 5 |
| 1447 | $$ a_1 = 1875 ~~,~~ r = \frac{ 1 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 5 |
| 1448 | $$ a_1 = 1875 ~,~ r = \frac{ 1 }{ 5 } ~,~ a_n = 9 ~,~ n = ? $$ | 5 |
| 1449 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = -2 $. | 5 |
| 1450 | Find $ a_5 $ of a geometric progression if $ a_1 = -113 ~~ \text{and} ~~ r = 6 $. | 5 |
