Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 2501 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $. | 3 |
| 2502 | $$ a_1 = 1 ~,~ r = 2 ~,~ a_n = 64 ~,~ n = ? $$ | 3 |
| 2503 | $$ a_1 = 8 ~,~ r = \frac{ 5 }{ 4 } ~,~ a_n = 8 ~,~ n = ? $$ | 3 |
| 2504 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $. | 3 |
| 2505 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $. | 3 |
| 2506 | Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 32 $. | 3 |
| 2507 | Find $ a_15 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 2 $. | 3 |
| 2508 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $. | 3 |
| 2509 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 15000000 ~~ \text{and} ~~ r = 0.9 $. | 3 |
| 2510 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $. | 3 |
| 2511 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 0.05 ~~ \text{and} ~~ r = 2 $. | 3 |
| 2512 | Find $ a_9 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 3 |
| 2513 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 1.05 $. | 3 |
| 2514 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $. | 3 |
| 2515 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $. | 3 |
| 2516 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 2 ~~ \text{and} ~~ a_{ 4 } = 54 $. | 3 |
| 2517 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 48 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 3 |
| 2518 | Find $ a_12 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 3 |
| 2519 | Find $ a_11 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 3 $. | 3 |
| 2520 | $$ a_1 = 46 ~,~ r = 1.003 ~,~ a_n = 16 ~,~ n = ? $$ | 3 |
| 2521 | Find $ a_7 $ of a geometric progression if $ a_1 = 375 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 3 |
| 2522 | Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $. | 3 |
| 2523 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $. | 3 |
| 2524 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 61 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 41 }{ 50 } $. | 3 |
| 2525 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 8 }{ 11 } $. | 3 |
| 2526 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 3 |
| 2527 | Find $ a_8 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 3 |
| 2528 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -1 $. | 3 |
| 2529 | Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -4 $. | 3 |
| 2530 | Find $ a_6 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -4 $. | 3 |
| 2531 | Find $ a_16 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $. | 3 |
| 2532 | Find $ a_12 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 3 |
| 2533 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 3 |
| 2534 | Find $ a_4 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $. | 3 |
| 2535 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -5 $. | 3 |
| 2536 | Find $ a_7 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 3 $. | 3 |
| 2537 | Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 10 $. | 3 |
| 2538 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 3 |
| 2539 | $$ a_1 = 6 ~,~ r = 3 ~,~ a_n = 13122 ~,~ n = ? $$ | 3 |
| 2540 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $. | 3 |
| 2541 | $$ a_1 = 810 ~,~ r = 1.667 ~,~ a_n = 7 ~,~ n = ? $$ | 3 |
| 2542 | Find $ a_7 $ of a geometric progression if $ a_1 = -64 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 3 |
| 2543 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = \frac{ 61 }{ 50 } $. | 3 |
| 2544 | Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 3 |
| 2545 | Find $ a_4 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -5 $. | 3 |
| 2546 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $. | 3 |
| 2547 | Find $ a_8 $ of a geometric progression if $ a_1 = 4096 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 3 |
| 2548 | Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = 5 $. | 3 |
| 2549 | Find $ a_6 $ of a geometric progression if $ a_1 = 540 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $. | 3 |
| 2550 | Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 3 |
