Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 10451 | Find $ a_2 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = -5 $. | 1 |
| 10452 | Find $ a_7 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -3 $. | 1 |
| 10453 | Find $ a_7 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10454 | Find $ a_11 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 40 } ~~ \text{and} ~~ r = -4 $. | 1 |
| 10455 | Find $ a_11 $ of a geometric progression if $ a_1 = 0.025 ~~ \text{and} ~~ r = -4 $. | 1 |
| 10456 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ r = 4 $. | 1 |
| 10457 | Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 1 |
| 10458 | Find $ a_5 $ of a geometric progression if $ a_1 = 48 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 1 |
| 10459 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 10460 | Find $ a_10 $ of a geometric progression if $ a_1 = 0.006 ~~ \text{and} ~~ r = 2 $. | 1 |
| 10461 | Find $ a_10 $ of a geometric progression if $ a_1 = 0.006 ~~ \text{and} ~~ r = 2 $. | 1 |
| 10462 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 9072 ~~ \text{and} ~~ a_{ 4 } = 5250 $. | 1 |
| 10463 | $$ a_1 = 9072 ~,~ r = 0.8333 ~,~ a_n = 7 ~,~ n = ? $$ | 1 |
| 10464 | Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 100 } ~~ \text{and} ~~ r = 10 $. | 1 |
| 10465 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 11200000000 ~~ \text{and} ~~ r = 1.54 $. | 1 |
| 10466 | Find $ a_10 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $. | 1 |
| 10467 | Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 10468 | Find $ a_3 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 10469 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10470 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $. | 1 |
| 10471 | Find $ a_10 $ of a geometric progression if $ a_1 = -162 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 1 |
| 10472 | $$ a_1 = 240000 ~,~ r = \frac{ 11 }{ 10 } ~,~ S_n = 940000 ~,~ n = ? $$ | 1 |
| 10473 | $$ a_1 = 1 ~,~ r = 2 ~,~ a_n = 52 ~,~ n = ? $$ | 1 |
| 10474 | Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 10475 | Find $ a_14 $ of a geometric progression if $ a_1 = \dfrac{ 10 }{ 3 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 10476 | Find $ a_5 $ of a geometric progression if $ a_1 = -90 ~~ \text{and} ~~ r = 2 $. | 1 |
| 10477 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 7 ~~ \text{and} ~~ a_{ 2 } = 21 $. | 1 |
| 10478 | $$ a_1 = 1 ~,~ r = 2 ~,~ a_n = 6 ~,~ n = ? $$ | 1 |
| 10479 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -14 ~~ \text{and} ~~ r = 4 $. | 1 |
| 10480 | Find the sum of the first $ 10000 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 10481 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 10482 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 5 } = 18 ~~ \text{and} ~~ a_{ 6 } = 54 $. | 1 |
| 10483 | Find $ a_7 $ of a geometric progression if $ a_1 = 6400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 10484 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6400 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 10485 | Find $ a_10 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -6 $. | 1 |
| 10486 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 16 } ~~ \text{and} ~~ r = \frac{ 5 }{ 256 } $. | 1 |
| 10487 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 4 }{ 7 } ~~ \text{and} ~~ a_{ 3 } = 7 $. | 1 |
| 10488 | $$ a_1 = -2 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 10489 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 4 $. | 1 |
| 10490 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 10491 | Find $ a_5 $ of a geometric progression if $ a_1 = 640 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 10492 | Find $ a_30 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 4 $. | 1 |
| 10493 | Find $ a_2 $ of a geometric progression if $ a_1 = 729 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 10494 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 2 ~~ \text{and} ~~ a_{ 7 } = 7 $. | 1 |
| 10495 | $$ a_1 = 30 ~,~ r = 4 ~,~ a_n = 30 ~,~ n = ? $$ | 1 |
| 10496 | Find $ a_12 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 10497 | Find $ a_9 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $. | 1 |
| 10498 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 1 |
| 10499 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 10500 | Find $ a_25 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
