Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 5001 | Find $ a_2 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 20 } $. | 2 |
| 5002 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 240 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $. | 2 |
| 5003 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 2 |
| 5004 | $$ a_1 = 960 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = 15 ~,~ n = ? $$ | 2 |
| 5005 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 300 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 2 |
| 5006 | $$ a_1 = \frac{ 2999 }{ 100 } ~,~ r = \frac{ 36 }{ 25 } ~,~ a_n = 100 ~,~ n = ? $$ | 2 |
| 5007 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 250 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 2 |
| 5008 | $$ a_1 = 24000 ~,~ r = \frac{ 3 }{ 20 } ~,~ a_n = 1.823 ~,~ n = ? $$ | 2 |
| 5009 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 10000000 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $. | 2 |
| 5010 | Find $ a_6 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 2 |
| 5011 | Find $ a_6 $ of a geometric progression if $ a_1 = 4000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 2 |
| 5012 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 4000 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $. | 2 |
| 5013 | $$ a_1 = 2 ~,~ r = 4 ~,~ S_n = 5 ~,~ n = ? $$ | 2 |
| 5014 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 5 }{ 3 } ~~ \text{and} ~~ a_{ 10 } = 5859375 $. | 2 |
| 5015 | Find $ a_15 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -3 $. | 2 |
| 5016 | Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 2 |
| 5017 | Find $ a_7 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 2 |
| 5018 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 24 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 37 }{ 50 } $. | 2 |
| 5019 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $. | 2 |
| 5020 | $$ a_1 = 3125 ~,~ r = \frac{ 1 }{ 5 } ~,~ a_n = 1 ~,~ n = ? $$ | 2 |
| 5021 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3125 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 2 |
| 5022 | $$ a_1 = \frac{ 1 }{ 3 } ~,~ r = \frac{ 2 }{ 3 } ~,~ a_n = 4 ~,~ n = ? $$ | 2 |
| 5023 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 20 } = 100 $. | 2 |
| 5024 | Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 1.1 ~~ \text{and} ~~ r = 1.1 $. | 2 |
| 5025 | Find $ a_8 $ of a geometric progression if $ a_1 = 4096 ~~ \text{and} ~~ r = 15.63 $. | 2 |
| 5026 | Find $ a_4 $ of a geometric progression if $ a_1 = 4096 ~~ \text{and} ~~ r = 15.63 $. | 2 |
| 5027 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $. | 2 |
| 5028 | Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 5029 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 12 } ~~ \text{and} ~~ r = -6 $. | 2 |
| 5030 | Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 3 } ~~ \text{and} ~~ r = -9 $. | 2 |
| 5031 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = -3 $. | 2 |
| 5032 | Find $ a_4 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $. | 2 |
| 5033 | Find $ a_13 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 5034 | Find $ a_2 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 11 $. | 2 |
| 5035 | Find the sum of the first $ 361 $ terms of a geometric sequence if $ a_1 = 3181 ~~ \text{and} ~~ r = 0.994 $. | 2 |
| 5036 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $. | 2 |
| 5037 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 7 } = 4800 ~~ \text{and} ~~ a_{ 3 } = 150 $. | 2 |
| 5038 | Find $ a_7 $ of a geometric progression if $ a_1 = 26.52 ~~ \text{and} ~~ r = 2.378 $. | 2 |
| 5039 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 500 ~~ \text{and} ~~ r = -15 $. | 2 |
| 5040 | Find $ a_7 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 2 |
| 5041 | Find $ a_62000 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $. | 2 |
| 5042 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1000 $. | 2 |
| 5043 | Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 2 |
| 5044 | Find $ a_16 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 0.632 $. | 2 |
| 5045 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $. | 2 |
| 5046 | Find $ a_4 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -6 $. | 2 |
| 5047 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 2 |
| 5048 | Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $. | 2 |
| 5049 | Find $ a_12 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $. | 2 |
| 5050 | Find $ a_12 $ of a geometric progression if $ a_1 = 250 ~~ \text{and} ~~ r = -40 $. | 2 |
