Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 7451 | Find $ a_14 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $. | 1 |
| 7452 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 7453 | $$ a_1 = 8 ~,~ r = \frac{ 1 }{ 4 } ~,~ a_n = 8 ~,~ n = ? $$ | 1 |
| 7454 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -12800 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 7455 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 16 } $. | 1 |
| 7456 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 51 }{ 50 } $. | 1 |
| 7457 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 3 } = 189 $. | 1 |
| 7458 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 17 ~~ \text{and} ~~ r = -3 $. | 1 |
| 7459 | Find $ a_5 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = 9 $. | 1 |
| 7460 | Find $ a_5 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 100 } $. | 1 |
| 7461 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 1 ~~ \text{and} ~~ a_{ 10 } = 378 $. | 1 |
| 7462 | Find the sum of the first $ 81920 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $. | 1 |
| 7463 | Find the sum of the first $ 49 $ terms of a geometric sequence if $ a_1 = 300 ~~ \text{and} ~~ r = 1.04 $. | 1 |
| 7464 | Find $ a_5 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 7465 | Find $ a_10 $ of a geometric progression if $ a_1 = 450 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 7466 | $$ a_1 = 450 ~~,~~ r = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 7467 | Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -7 $. | 1 |
| 7468 | Find $ a_9 $ of a geometric progression if $ a_1 = 3200 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 7469 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 0.01 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7470 | $$ a_1 = 3 ~,~ r = 2 ~,~ S_n = 50000 ~,~ n = ? $$ | 1 |
| 7471 | Find $ a_5 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7472 | Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 4 $. | 1 |
| 7473 | Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 4 } $. | 1 |
| 7474 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 9 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 7475 | Find $ a_3 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7476 | Find $ a_7 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 6 } $. | 1 |
| 7477 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 25 } ~~ \text{and} ~~ r = 5 $. | 1 |
| 7478 | Find $ a_729 $ of a geometric progression if $ a_1 = 1.5 ~~ \text{and} ~~ r = 3 $. | 1 |
| 7479 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 4 }{ 5 } $. | 1 |
| 7480 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 0.3518 ~~ \text{and} ~~ r = -0.8 $. | 1 |
| 7481 | Find $ a_15 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -0.8 $. | 1 |
| 7482 | Find $ a_15 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 5 } $. | 1 |
| 7483 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 102 ~~ \text{and} ~~ r = \frac{ 23 }{ 10 } $. | 1 |
| 7484 | $$ a_1 = 32 ~~,~~ r = \frac{ 4 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 7485 | Find $ a_12 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 7486 | Find $ a_12 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = 0.8 $. | 1 |
| 7487 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 8 } = \frac{ 41 }{ 8 } ~~ \text{and} ~~ a_{ 12 } = 82 $. | 1 |
| 7488 | Find $ a_5 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7489 | Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 5 $. | 1 |
| 7490 | Find $ a_1 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -7 $. | 1 |
| 7491 | Find $ a_2 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -7 $. | 1 |
| 7492 | Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -7 $. | 1 |
| 7493 | Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -7 $. | 1 |
| 7494 | Find $ a_12 $ of a geometric progression if $ a_1 = 300 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $. | 1 |
| 7495 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 800 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 7496 | Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 7497 | Find $ a_11 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 7498 | Find $ a_11 $ of a geometric progression if $ a_1 = -128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 7499 | Find $ a_11 $ of a geometric progression if $ a_1 = -128 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 1 |
| 7500 | Find $ a_8 $ of a geometric progression if $ a_1 = 1400 ~~ \text{and} ~~ r = \dfrac{ 22 }{ 25 } $. | 1 |
