Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 7051 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -3 $. | 1 |
| 7052 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 7053 | Find $ a_6 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 16 } $. | 1 |
| 7054 | Find $ a_4 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -2 $. | 1 |
| 7055 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $. | 1 |
| 7056 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 16 ~~ \text{and} ~~ a_{ 4 } = \frac{ 27 }{ 4 } $. | 1 |
| 7057 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 6 }{ 7 } $. | 1 |
| 7058 | Find the sum of the first $ 37 $ terms of a geometric sequence if $ a_1 = 123600 ~~ \text{and} ~~ r = 1.05 $. | 1 |
| 7059 | Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $. | 1 |
| 7060 | $$ a_1 = 5 ~,~ r = 2 ~,~ a_n = 10 ~,~ n = ? $$ | 1 |
| 7061 | Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 20000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 7062 | Find $ a_3 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 10 $. | 1 |
| 7063 | Find $ a_10 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = -2 $. | 1 |
| 7064 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 45 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $. | 1 |
| 7065 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 48547 ~~ \text{and} ~~ r = 1.15 $. | 1 |
| 7066 | $$ a_1 = 0.1 ~~,~~ r = 2.5 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 7067 | $$ a_1 = 0.1 ~,~ r = 2.5 ~,~ S_n = 100 ~,~ n = ? $$ | 1 |
| 7068 | $$ a_1 = 1 ~~,~~ r = 2 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 7069 | $$ a_1 = 6.58E-6 ~,~ r = \frac{ 29 }{ 20 } ~,~ a_n = 13 ~,~ n = ? $$ | 1 |
| 7070 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 221253 ~~ \text{and} ~~ r = 1.021 $. | 1 |
| 7071 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 1 } = 17 ~~ \text{and} ~~ a_{ 7 } = 43 $. | 1 |
| 7072 | Find $ a_5 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = 1.167 $. | 1 |
| 7073 | Find $ a_7 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 7074 | Find $ a_10 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 5 $. | 1 |
| 7075 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 7076 | Find $ a_2 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $. | 1 |
| 7077 | Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 8 } $. | 1 |
| 7078 | Find $ a_10 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 7079 | Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 7080 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $. | 1 |
| 7081 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = -2 $. | 1 |
| 7082 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -15 ~~ \text{and} ~~ r = -2 $. | 1 |
| 7083 | Find $ a_7 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = 1.09 $. | 1 |
| 7084 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $. | 1 |
| 7085 | Find $ a_21 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $. | 1 |
| 7086 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1451 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 7087 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -12 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 7088 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 7089 | Find $ a_9 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7090 | Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $. | 1 |
| 7091 | Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 7092 | Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 7093 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 7094 | Find $ a_400 $ of a geometric progression if $ a_1 = 300 ~~ \text{and} ~~ r = 1.015 $. | 1 |
| 7095 | Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 1 |
| 7096 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 1 |
| 7097 | Find $ a_500 $ of a geometric progression if $ a_1 = 300 ~~ \text{and} ~~ r = 1.02 $. | 1 |
| 7098 | Find $ a_14 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 0.83 $. | 1 |
| 7099 | Find $ a_100 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = -2 $. | 1 |
| 7100 | Find $ a_100 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
