Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 8101 | Find $ a_9 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = 5 $. | 1 |
| 8102 | Find $ a_1 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 8103 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -5 $. | 1 |
| 8104 | Find $ a_12 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 1.5 $. | 1 |
| 8105 | Find $ a_2 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 27 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 243 } $. | 1 |
| 8106 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 1 }{ 2 } ~~ \text{and} ~~ a_{ 2 } = 8 $. | 1 |
| 8107 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 3 } = \frac{ 175 }{ 4 } ~~ \text{and} ~~ a_{ 4 } = \frac{ 875 }{ 8 } $. | 1 |
| 8108 | Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $. | 1 |
| 8109 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 3 } = \frac{ 75 }{ 16 } ~~ \text{and} ~~ a_{ 4 } = \frac{ 375 }{ 64 } $. | 1 |
| 8110 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 32805 ~~ \text{and} ~~ a_{ 2 } = 3645 $. | 1 |
| 8111 | Find $ a_8 $ of a geometric progression if $ a_1 = 32805 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 9 } $. | 1 |
| 8112 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 8113 | $$ a_1 = 20 ~,~ r = \frac{ 9 }{ 10 } ~,~ S_n = \frac{ 8853 }{ 20 } ~,~ n = ? $$ | 1 |
| 8114 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $. | 1 |
| 8115 | Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 480 ~~ \text{and} ~~ r = 1.01 $. | 1 |
| 8116 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 8 } ~~ \text{and} ~~ r = 4 $. | 1 |
| 8117 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = -\frac{ 1 }{ 10 } $. | 1 |
| 8118 | $$ a_1 = 1 ~~,~~ r = 7 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 8119 | $$ a_1 = 8 ~,~ r = 2 ~,~ a_n = 22 ~,~ n = ? $$ | 1 |
| 8120 | Find $ a_22 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8121 | Find $ a_7 $ of a geometric progression if $ a_1 = 1000000000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $. | 1 |
| 8122 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8123 | Find $ a_7 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 20 } $. | 1 |
| 8124 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 8125 | Find $ a_9 $ of a geometric progression if $ a_1 = 240 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 1 |
| 8126 | Find $ a_2 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8127 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $. | 1 |
| 8128 | Find $ a_4 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8129 | Find $ a_4 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 8130 | Find $ a_4 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = 1.5 $. | 1 |
| 8131 | Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 8132 | Find $ a_1 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 4 } $. | 1 |
| 8133 | Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8134 | Find $ a_30 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = 1.08 $. | 1 |
| 8135 | Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 8136 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 8137 | Find $ a_32 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -1 $. | 1 |
| 8138 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1500 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8139 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1512 ~~ \text{and} ~~ r = 6 $. | 1 |
| 8140 | Find $ a_10 $ of a geometric progression if $ a_1 = -12 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8141 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -12 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8142 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8143 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -1 $. | 1 |
| 8144 | Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -1 $. | 1 |
| 8145 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 5 ~~ \text{and} ~~ a_{ 1 } = 3 $. | 1 |
| 8146 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 5 ~~ \text{and} ~~ a_{ 3 } = 3 $. | 1 |
| 8147 | Find $ a_45 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 0.9808 $. | 1 |
| 8148 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 8 }{ 5 } ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $. | 1 |
| 8149 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 262144 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $. | 1 |
| 8150 | $$ a_1 = \frac{ 5 }{ 2 } ~,~ r = 2 ~,~ a_n = 11 ~,~ n = ? $$ | 1 |
