Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 8601 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 19 ~~ \text{and} ~~ r = -5 $. | 1 |
| 8602 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 125 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $. | 1 |
| 8603 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 125 ~~ \text{and} ~~ r = 5 $. | 1 |
| 8604 | Find $ a_7 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = -1.333 $. | 1 |
| 8605 | Find $ a_8 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 4.348 $. | 1 |
| 8606 | Find $ a_7 $ of a geometric progression if $ a_1 = 270 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 8607 | Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $. | 1 |
| 8608 | Find $ a_4 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8609 | Find the sum of the first $ 23 $ terms of a geometric sequence if $ a_1 = 80 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 8610 | Find $ a_6 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = 4 $. | 1 |
| 8611 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 8612 | Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8613 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8614 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 228 ~~ \text{and} ~~ r = \frac{ 24 }{ 5 } $. | 1 |
| 8615 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8616 | Find $ a_1 $ of a geometric progression if $ a_1 = 11000 ~~ \text{and} ~~ r = 0.03 $. | 1 |
| 8617 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 95 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 8618 | Find $ a_7 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = 5 $. | 1 |
| 8619 | $$ a_1 = -1 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 8620 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8621 | Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 10 $. | 1 |
| 8622 | Find $ a_9 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8623 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $. | 1 |
| 8624 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $. | 1 |
| 8625 | Find $ a_9 $ of a geometric progression if $ a_1 = 14000 ~~ \text{and} ~~ r = 0.015 $. | 1 |
| 8626 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8627 | Find $ a_13 $ of a geometric progression if $ a_1 = 42 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 8628 | Find $ a_5 $ of a geometric progression if $ a_1 = 42 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 8629 | Find $ a_8 $ of a geometric progression if $ a_1 = 1715 ~~ \text{and} ~~ r = 7 $. | 1 |
| 8630 | Find $ a_4 $ of a geometric progression if $ a_1 = -192 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 8631 | Find $ a_6 $ of a geometric progression if $ a_1 = 224 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8632 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $. | 1 |
| 8633 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 16 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 8634 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 16 } ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $. | 1 |
| 8635 | Find $ a_5 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 5 $. | 1 |
| 8636 | $$ a_1 = 10 ~,~ r = \frac{ 61 }{ 50 } ~,~ S_n = 360 ~,~ n = ? $$ | 1 |
| 8637 | $$ a_1 = 10 ~,~ r = \frac{ 61 }{ 50 } ~,~ a_n = 360 ~,~ n = ? $$ | 1 |
| 8638 | Find $ a_5 $ of a geometric progression if $ a_1 = 11000 ~~ \text{and} ~~ r = \dfrac{ 101 }{ 100 } $. | 1 |
| 8639 | Find $ a_10 $ of a geometric progression if $ a_1 = 100000 ~~ \text{and} ~~ r = 0.05 $. | 1 |
| 8640 | Find the sum of the first $ 200 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 8641 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 1 } = 3 ~~ \text{and} ~~ a_{ 4 } = 17 $. | 1 |
| 8642 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 8643 | $$ a_1 = 12 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 8644 | Find $ a_2 $ of a geometric progression if $ a_1 = 100000 ~~ \text{and} ~~ r = \dfrac{ 17 }{ 10 } $. | 1 |
| 8645 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 100000 ~~ \text{and} ~~ r = \frac{ 17 }{ 10 } $. | 1 |
| 8646 | Find $ a_1 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 1 |
| 8647 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 16 } ~~ \text{and} ~~ r = \frac{ 1 }{ 128 } $. | 1 |
| 8648 | Find $ a_5 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 4 $. | 1 |
| 8649 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = 1.05 $. | 1 |
| 8650 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 0.002739 ~~ \text{and} ~~ r = 0.002739 $. | 1 |
