Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 8251 | Find $ a_4 $ of a geometric progression if $ a_1 = 42 ~~ \text{and} ~~ r = -8 $. | 1 |
| 8252 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $. | 1 |
| 8253 | Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $. | 1 |
| 8254 | Find $ a_6 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 8255 | Find $ a_2 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 8256 | Find $ a_3 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 8257 | Find $ a_4 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 8258 | Find $ a_12 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -6 $. | 1 |
| 8259 | $$ a_1 = 10 ~,~ r = 0.333 ~,~ a_n = 2222 ~,~ n = ? $$ | 1 |
| 8260 | $$ a_1 = 10 ~,~ r = 1.5 ~,~ a_n = 1490 ~,~ n = ? $$ | 1 |
| 8261 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 8262 | Find $ a_3 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8263 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 1 |
| 8264 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 1 }{ 3 } ~~ \text{and} ~~ a_{ 6 } = 443 $. | 1 |
| 8265 | $$ a_1 = 16 ~,~ r = \frac{ 1 }{ 2 } ~,~ S_n = 31.94 ~,~ n = ? $$ | 1 |
| 8266 | Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 8267 | Find $ a_15 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 8268 | Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $. | 1 |
| 8269 | Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 8270 | Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 8271 | Find $ a_12 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 8272 | Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 8273 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 1.3 $. | 1 |
| 8274 | Find the sum of the first $ 38 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8275 | Find $ a_5 $ of a geometric progression if $ a_1 = 40000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 20 } $. | 1 |
| 8276 | Find $ a_14 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8277 | Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 5 $. | 1 |
| 8278 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 70000 ~~ \text{and} ~~ r = 1.015 $. | 1 |
| 8279 | Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8280 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 6 ~~ \text{and} ~~ a_{ 3 } = 16 $. | 1 |
| 8281 | Find $ a_10 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 4 $. | 1 |
| 8282 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 43 ~~ \text{and} ~~ a_{ 2 } = 38 $. | 1 |
| 8283 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 8284 | Find $ a_1 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8285 | $$ a_1 = 2 ~,~ r = 2 ~,~ S_n = 14 ~,~ n = ? $$ | 1 |
| 8286 | $$ a_1 = 6 ~~,~~ r = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 8287 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 125 } ~~ \text{and} ~~ r = 5 $. | 1 |
| 8288 | Find $ a_7 $ of a geometric progression if $ a_1 = 0.0008 ~~ \text{and} ~~ r = -10 $. | 1 |
| 8289 | Find $ a_13 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $. | 1 |
| 8290 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 8291 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 10 $. | 1 |
| 8292 | Find $ a_14 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8293 | Find $ a_15 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8294 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.9 $. | 1 |
| 8295 | Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 6 $. | 1 |
| 8296 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8297 | Find the sum of the first $ 99999 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ r = \frac{ 7 }{ 10 } $. | 1 |
| 8298 | Find the sum of the first $ 999 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ r = \frac{ 7 }{ 10 } $. | 1 |
| 8299 | Find the sum of the first $ 99 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ r = \frac{ 7 }{ 10 } $. | 1 |
| 8300 | Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $. | 1 |
