Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 7601 | Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.8625 $. | 1 |
| 7602 | Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 8.625 $. | 1 |
| 7603 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 15000 ~~ \text{and} ~~ r = 1.12 $. | 1 |
| 7604 | Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.0325 $. | 1 |
| 7605 | Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.325 $. | 1 |
| 7606 | Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.325 $. | 1 |
| 7607 | Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.1375 $. | 1 |
| 7608 | Find $ a_12 $ of a geometric progression if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.01375 $. | 1 |
| 7609 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 20700 ~~ \text{and} ~~ r = 0.1375 $. | 1 |
| 7610 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 7611 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = -\frac{ 2 }{ 5 } $. | 1 |
| 7612 | $$ a_1 = 7 ~,~ r = 4 ~,~ a_n = 114688 ~,~ n = ? $$ | 1 |
| 7613 | $$ a_1 = 4 ~,~ r = 2 ~,~ a_n = 524288 ~,~ n = ? $$ | 1 |
| 7614 | Find $ a_5 $ of a geometric progression if $ a_1 = 58 ~~ \text{and} ~~ r = 15 $. | 1 |
| 7615 | Find $ a_3 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $. | 1 |
| 7616 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $. | 1 |
| 7617 | Find $ a_3 $ of a geometric progression if $ a_1 = -54 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $. | 1 |
| 7618 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $. | 1 |
| 7619 | Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.9 $. | 1 |
| 7620 | Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.9 $. | 1 |
| 7621 | $$ a_1 = 5 ~,~ r = 2 ~,~ a_n = 1 ~,~ n = ? $$ | 1 |
| 7622 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 22 }{ 5 } $. | 1 |
| 7623 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $. | 1 |
| 7624 | Find $ a_20 $ of a geometric progression if $ a_1 = 23400000000 ~~ \text{and} ~~ r = 1.8 $. | 1 |
| 7625 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $. | 1 |
| 7626 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 7627 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 12 ~~ \text{and} ~~ a_{ 4 } = \frac{ 4 }{ 3 } $. | 1 |
| 7628 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 5 ~~ \text{and} ~~ a_{ 3 } = 80 $. | 1 |
| 7629 | Find $ a_12 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $. | 1 |
| 7630 | $$ a_1 = 1 ~,~ r = 2 ~,~ a_n = 128 ~,~ n = ? $$ | 1 |
| 7631 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 200000 ~~ \text{and} ~~ r = 0.06 $. | 1 |
| 7632 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 150000 ~~ \text{and} ~~ r = -0.5 $. | 1 |
| 7633 | Find $ a_1 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 7634 | Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7635 | Find $ a_10 $ of a geometric progression if $ a_1 = 70 ~~ \text{and} ~~ r = 3 $. | 1 |
| 7636 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 80 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 7637 | Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 7638 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 7639 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 7640 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 7641 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 7642 | Find $ a_3 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 7643 | Find $ a_6 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 7644 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 0.333 $. | 1 |
| 7645 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 0.333 $. | 1 |
| 7646 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 250 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 7647 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 250 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 7648 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 250 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 7649 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 9 ~~ \text{and} ~~ a_{ 2 } = 36 $. | 1 |
| 7650 | Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 3 $. | 1 |
