Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 10001 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10002 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10003 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10004 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10005 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10006 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10007 | Find $ a_5 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 10008 | Find $ a_4 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 10009 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10010 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 34 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10011 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 10012 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $. | 1 |
| 10013 | Find $ a_8 $ of a geometric progression if $ a_1 = -20 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 10014 | Find $ a_9 $ of a geometric progression if $ a_1 = -20 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 10015 | Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 10016 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 45 ~~ \text{and} ~~ r = 1.087 $. | 1 |
| 10017 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 92 ~~ \text{and} ~~ r = 1.778 $. | 1 |
| 10018 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 92 ~~ \text{and} ~~ r = 1.778 $. | 1 |
| 10019 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3280 ~~ \text{and} ~~ r = \frac{ 3 }{ 10 } $. | 1 |
| 10020 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3280 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10021 | Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 3280 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10022 | Find $ a_8 $ of a geometric progression if $ a_1 = 140 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10023 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 140 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10024 | Find $ a_8 $ of a geometric progression if $ a_1 = 3280 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $. | 1 |
| 10025 | Find $ a_8 $ of a geometric progression if $ a_1 = 3280 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10026 | Find $ a_5 $ of a geometric progression if $ a_1 = 3280 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10027 | Find $ a_5 $ of a geometric progression if $ a_1 = 3280 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10028 | Find $ a_8 $ of a geometric progression if $ a_1 = 410 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10029 | $$ a_1 = 3280 ~,~ r = 3 ~,~ S_n = 3280 ~,~ n = ? $$ | 1 |
| 10030 | $$ a_1 = 3280 ~,~ r = 3 ~,~ S_n = 8 ~,~ n = ? $$ | 1 |
| 10031 | $$ a_1 = 8 ~,~ r = 3 ~,~ S_n = 3280 ~,~ n = ? $$ | 1 |
| 10032 | $$ a_1 = 8 ~,~ r = 3 ~,~ a_n = 3280 ~,~ n = ? $$ | 1 |
| 10033 | Find the sum of the first $ 51 $ terms of a geometric sequence if $ a_1 = 31.8 ~~ \text{and} ~~ r = 1.06 $. | 1 |
| 10034 | Find $ a_5 $ of a geometric progression if $ a_1 = 139703 ~~ \text{and} ~~ r = 0.0328 $. | 1 |
| 10035 | Find $ a_9 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 1 |
| 10036 | Find $ a_11 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 10037 | Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10038 | Find $ a_12 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 10039 | Find $ a_16 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 10040 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = -6 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 10041 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 5 } ~~ \text{and} ~~ r = -3 $. | 1 |
| 10042 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ r = -2 $. | 1 |
| 10043 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 1 ~~ \text{and} ~~ a_{ 4 } = \frac{ 1 }{ 81 } $. | 1 |
| 10044 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 21 ~~ \text{and} ~~ r = 0.1111 $. | 1 |
| 10045 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = 9 $. | 1 |
| 10046 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = 9 $. | 1 |
| 10047 | Find $ a_31 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $. | 1 |
| 10048 | Find the sum of the first $ 100000000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 10049 | Find the sum of the first $ 100000000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -0.5 $. | 1 |
| 10050 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
