Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 7001 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 1 |
| 7002 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $. | 1 |
| 7003 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 24000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $. | 1 |
| 7004 | Find $ a_60 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.011 $. | 1 |
| 7005 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $. | 1 |
| 7006 | Find $ a_5 $ of a geometric progression if $ a_1 = 608 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 7007 | Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -11 $. | 1 |
| 7008 | Find $ a_6 $ of a geometric progression if $ a_1 = 495000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $. | 1 |
| 7009 | $$ a_1 = 256 ~,~ r = \frac{ 3 }{ 4 } ~,~ S_n = 13 ~,~ n = ? $$ | 1 |
| 7010 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 7011 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 11 }{ 50 } $. | 1 |
| 7012 | Find $ a_10 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = -6 $. | 1 |
| 7013 | Find $ a_2 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = -6 $. | 1 |
| 7014 | Find $ a_2 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $. | 1 |
| 7015 | Find $ a_3 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $. | 1 |
| 7016 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 4 ~~ \text{and} ~~ a_{ 5 } = 1792 $. | 1 |
| 7017 | Find $ a_25 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7018 | $$ a_1 = 1000 ~,~ r = 2 ~,~ a_n = 7 ~,~ n = ? $$ | 1 |
| 7019 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 6 }{ 7 } $. | 1 |
| 7020 | Find $ a_4 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 4 $. | 1 |
| 7021 | Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 5 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 7022 | $$ a_1 = 3 ~,~ r = 2 ~,~ a_n = 196608 ~,~ n = ? $$ | 1 |
| 7023 | Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7024 | Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $. | 1 |
| 7025 | Find $ a_11 $ of a geometric progression if $ a_1 = 144 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 7026 | $$ a_1 = 8 ~~,~~ r = 13 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 7027 | $$ a_1 = 8 ~,~ r = 13 ~,~ a_n = 5 ~,~ n = ? $$ | 1 |
| 7028 | $$ a_1 = 8 ~,~ r = 13 ~,~ S_n = 5 ~,~ n = ? $$ | 1 |
| 7029 | Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 19 } $. | 1 |
| 7030 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 7031 | Find $ a_9 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 7032 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 7033 | Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 7034 | Find $ a_5 $ of a geometric progression if $ a_1 = -100 ~~ \text{and} ~~ r = -3 $. | 1 |
| 7035 | Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 100 } $. | 1 |
| 7036 | Find $ a_3 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = 0.1667 $. | 1 |
| 7037 | Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7038 | $$ a_1 = 25 ~,~ r = 3 ~,~ a_n = 5 ~,~ n = ? $$ | 1 |
| 7039 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7040 | Find $ a_6 $ of a geometric progression if $ a_1 = -1024 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 8 } $. | 1 |
| 7041 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 7042 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 7043 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 7044 | Find $ a_4 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 7045 | Find $ a_4 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 7046 | Find $ a_10 $ of a geometric progression if $ a_1 = 24000 ~~ \text{and} ~~ r = 1.08 $. | 1 |
| 7047 | $$ a_1 = 5 ~,~ r = \frac{ 1 }{ 3 } ~,~ a_n = 9 ~,~ n = ? $$ | 1 |
| 7048 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $. | 1 |
| 7049 | Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 7050 | Find $ a_12 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -3 $. | 1 |
