Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 8501 | Find $ a_15 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8502 | Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8503 | Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 8504 | Find $ a_100 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 8505 | Find $ a_50 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 8506 | Find $ a_60 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 8507 | Find $ a_70 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 8508 | Find $ a_7 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8509 | Find $ a_10 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8510 | Find $ a_12 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8511 | Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 24 $. | 1 |
| 8512 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 8 }{ 5 } ~~ \text{and} ~~ r = 0.7753 $. | 1 |
| 8513 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $. | 1 |
| 8514 | Find the sum of the first $ 180 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 6 } ~~ \text{and} ~~ r = \frac{ 5 }{ 6 } $. | 1 |
| 8515 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 7 } $. | 1 |
| 8516 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 8517 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8518 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 320 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 8519 | Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8520 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 1.333 $. | 1 |
| 8521 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -21 ~~ \text{and} ~~ r = -7 $. | 1 |
| 8522 | Find $ a_6 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8523 | Find $ a_20 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8524 | Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 8525 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 8526 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 8527 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8528 | $$ a_1 = 6 ~,~ r = 3 ~,~ S_n = 531438 ~,~ n = ? $$ | 1 |
| 8529 | Find $ a_20 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8530 | $$ a_1 = 3 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 8531 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2592 ~~ \text{and} ~~ r = \frac{ 1 }{ 6 } $. | 1 |
| 8532 | Find $ a_10 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 8533 | Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 0.25 ~~ \text{and} ~~ r = 0.75 $. | 1 |
| 8534 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8535 | Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 16 }{ 5 } ~~ \text{and} ~~ r = -12 $. | 1 |
| 8536 | Find $ a_40 $ of a geometric progression if $ a_1 = 7000 ~~ \text{and} ~~ r = 1.058 $. | 1 |
| 8537 | Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 7000 ~~ \text{and} ~~ r = 1.058 $. | 1 |
| 8538 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 27 }{ 25 } $. | 1 |
| 8539 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8540 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1800 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 8541 | Find $ a_14 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = -3 $. | 1 |
| 8542 | Find $ a_14 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8543 | Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 16 } $. | 1 |
| 8544 | Find $ a_3 $ of a geometric progression if $ a_1 = 236 ~~ \text{and} ~~ r = 4 $. | 1 |
| 8545 | Find $ a_3 $ of a geometric progression if $ a_1 = 236 ~~ \text{and} ~~ r = -4 $. | 1 |
| 8546 | Find $ a_2 $ of a geometric progression if $ a_1 = 236 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 8547 | Find $ a_3 $ of a geometric progression if $ a_1 = 236 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 8548 | Find $ a_4 $ of a geometric progression if $ a_1 = 236 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 8549 | $$ a_1 = 1.0E-5 ~,~ r = \frac{ 11 }{ 10 } ~,~ S_n = 80 ~,~ n = ? $$ | 1 |
| 8550 | $$ a_1 = 1.0E-5 ~~,~~ r = \frac{ 11 }{ 10 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
