Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 8451 | Find $ a_9 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 2 } $. | 1 |
| 8452 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = 3.5 $. | 1 |
| 8453 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $. | 1 |
| 8454 | Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $. | 1 |
| 8455 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $. | 1 |
| 8456 | Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 8 $. | 1 |
| 8457 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $. | 1 |
| 8458 | $$ a_1 = 20 ~,~ r = \frac{ 1 }{ 4 } ~,~ S_n = \frac{ 4095 }{ 256 } ~,~ n = ? $$ | 1 |
| 8459 | $$ a_1 = 20 ~,~ r = \frac{ 2 }{ 5 } ~,~ S_n = \frac{ 4095 }{ 256 } ~,~ n = ? $$ | 1 |
| 8460 | Find $ a_19 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $. | 1 |
| 8461 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 0.08 $. | 1 |
| 8462 | $$ a_1 = 1 ~~,~~ r = 64 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 8463 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 27 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $. | 1 |
| 8464 | Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 107 }{ 100 } $. | 1 |
| 8465 | Find $ a_10 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 1.07 $. | 1 |
| 8466 | Find $ a_11 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 1.07 $. | 1 |
| 8467 | Find $ a_1 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 8468 | Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 1 |
| 8469 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 28 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 8470 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -15 ~~ \text{and} ~~ r = -1 $. | 1 |
| 8471 | Find $ a_6 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8472 | Find $ a_4 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8473 | Find $ a_10 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $. | 1 |
| 8474 | Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 18 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $. | 1 |
| 8475 | Find $ a_100 $ of a geometric progression if $ a_1 = -3.6 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 8476 | Find $ a_5 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $. | 1 |
| 8477 | Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 8478 | Find $ a_15 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 8479 | $$ a_1 = 5 ~,~ r = \frac{ 3 }{ 2 } ~,~ a_n = 6 ~,~ n = ? $$ | 1 |
| 8480 | Find $ a_5 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8481 | Find $ a_18 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8482 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8483 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 6 } $. | 1 |
| 8484 | Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 8485 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $. | 1 |
| 8486 | Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8487 | $$ a_1 = \frac{ 1 }{ 3 } ~~,~~ r = \frac{ 1 }{ 3 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 8488 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 8489 | Find $ a_29 $ of a geometric progression if $ a_1 = 192000 ~~ \text{and} ~~ r = 1.02 $. | 1 |
| 8490 | Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 192000 ~~ \text{and} ~~ r = 1.02 $. | 1 |
| 8491 | Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $. | 1 |
| 8492 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 3 }{ 10 } $. | 1 |
| 8493 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 1 } = \frac{ 12843 }{ 10 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 2583 }{ 2 } $. | 1 |
| 8494 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 1 } = 1284 ~~ \text{and} ~~ a_{ 2 } = 1292 $. | 1 |
| 8495 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 1284 ~~ \text{and} ~~ a_{ 3 } = 1292 $. | 1 |
| 8496 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 10 } ~~ \text{and} ~~ r = 1 $. | 1 |
| 8497 | Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 1 |
| 8498 | Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 8499 | Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 0.2 $. | 1 |
| 8500 | Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.2 $. | 1 |
