Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 4251 | Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 2 |
| 4252 | Find $ a_20 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 2 |
| 4253 | Find $ a_24 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $. | 2 |
| 4254 | Find $ a_50 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $. | 2 |
| 4255 | Find $ a_4 $ of a geometric progression if $ a_1 = -12 ~~ \text{and} ~~ r = 4 $. | 2 |
| 4256 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 17 }{ 250 } ~~ \text{and} ~~ r = \frac{ 17 }{ 25 } $. | 2 |
| 4257 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = \frac{ 17 }{ 250 } ~~ \text{and} ~~ r = \frac{ 17 }{ 25 } $. | 2 |
| 4258 | Find $ a_60 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $. | 2 |
| 4259 | Find $ a_65 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $. | 2 |
| 4260 | Find $ a_63 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $. | 2 |
| 4261 | Find $ a_15 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $. | 2 |
| 4262 | Find $ a_20 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 9 } ~~ \text{and} ~~ r = 3 $. | 2 |
| 4263 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = -\frac{ 5 }{ 8 } ~~ \text{and} ~~ a_{ 8 } = \frac{ 1 }{ 2 } $. | 2 |
| 4264 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 4 } = 3 ~~ \text{and} ~~ a_{ 7 } = 9 $. | 2 |
| 4265 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 36 }{ 25 } ~~ \text{and} ~~ a_{ 4 } = 3 $. | 2 |
| 4266 | Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -4 $. | 2 |
| 4267 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 3 } = \frac{ 3 }{ 4 } ~~ \text{and} ~~ a_{ 8 } = \frac{ 729 }{ 128 } $. | 2 |
| 4268 | Find $ a_15 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 2 |
| 4269 | Find $ a_15 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 2 |
| 4270 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1600 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 2 |
| 4271 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 4272 | Find $ a_10 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 2 |
| 4273 | Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 480 ~~ \text{and} ~~ r = 1.008 $. | 2 |
| 4274 | Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 480 ~~ \text{and} ~~ r = 1.009 $. | 2 |
| 4275 | Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 480 ~~ \text{and} ~~ r = 1.01 $. | 2 |
| 4276 | Find $ a_64 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $. | 2 |
| 4277 | Find $ a_64 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.5 $. | 2 |
| 4278 | $$ a_1 = 11 ~~,~~ r = 33 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 2 |
| 4279 | $$ a_1 = 11 ~~,~~ r = 33 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 2 |
| 4280 | $$ a_1 = 1 ~~,~~ r = 51 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 2 |
| 4281 | Find $ a_6 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 10 $. | 2 |
| 4282 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = 10 $. | 2 |
| 4283 | Find $ a_6 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 3 $. | 2 |
| 4284 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $. | 2 |
| 4285 | Find $ a_10 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 0.35 $. | 2 |
| 4286 | Find $ a_1 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -4 $. | 2 |
| 4287 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 2 |
| 4288 | Find $ a_5 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $. | 2 |
| 4289 | Find $ a_3 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = 3 $. | 2 |
| 4290 | Find $ a_6 $ of a geometric progression if $ a_1 = -8100 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 10 } $. | 2 |
| 4291 | Find $ a_4 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = 2 $. | 2 |
| 4292 | Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $. | 2 |
| 4293 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 1 } = 48 ~~ \text{and} ~~ a_{ 5 } = \frac{ 243 }{ 16 } $. | 2 |
| 4294 | $$ a_1 = 48 ~,~ r = \frac{ 3 }{ 4 } ~,~ a_n = \frac{ 243 }{ 16 } ~,~ n = ? $$ | 2 |
| 4295 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 1 } = 120 ~~ \text{and} ~~ a_{ 3 } = \frac{ 160 }{ 3 } $. | 2 |
| 4296 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 2 |
| 4297 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $. | 2 |
| 4298 | Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 8 } $. | 2 |
| 4299 | Find $ a_4 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $. | 2 |
| 4300 | Find $ a_1 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
