Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 9251 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 53 }{ 50 } $. | 1 |
| 9252 | Find the sum of the first $ 16384 $ terms of a geometric sequence if $ a_1 = -16 ~~ \text{and} ~~ r = -4 $. | 1 |
| 9253 | $$ a_1 = 4.1 ~,~ r = 2 ~,~ a_n = 61.5 ~,~ n = ? $$ | 1 |
| 9254 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 41000000000 ~~ \text{and} ~~ r = 1.03 $. | 1 |
| 9255 | Find $ a_9223372036854775807 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 9256 | Find $ a_18 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 0.5774 $. | 1 |
| 9257 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -\frac{ 4 }{ 5 } $. | 1 |
| 9258 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 5 ~~ \text{and} ~~ a_{ 4 } = 500 $. | 1 |
| 9259 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 4 } = 500 ~~ \text{and} ~~ a_{ 7 } = 62500 $. | 1 |
| 9260 | Find $ a_3 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -1 $. | 1 |
| 9261 | Find $ a_3 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 9262 | Find $ a_12 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -5 $. | 1 |
| 9263 | Find $ a_10 $ of a geometric progression if $ a_1 = 0.375 ~~ \text{and} ~~ r = 8 $. | 1 |
| 9264 | Find $ a_10 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 9265 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 9 } ~~ \text{and} ~~ r = -3 $. | 1 |
| 9266 | Find $ a_10 $ of a geometric progression if $ a_1 = -270 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 9267 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 9268 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 2 }{ 3 } ~~ \text{and} ~~ a_{ 5 } = 32 $. | 1 |
| 9269 | Find $ a_2 $ of a geometric progression if $ a_1 = 75000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 9270 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 75000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 9271 | Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 75000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 9272 | Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 75000 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 1 |
| 9273 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $. | 1 |
| 9274 | Find $ a_16 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 9 $. | 1 |
| 9275 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $. | 1 |
| 9276 | Find $ a_4 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 1 |
| 9277 | Find $ a_99999999 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $. | 1 |
| 9278 | Find $ a_1 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 9279 | $$ a_1 = 1 ~,~ r = 2 ~,~ a_n = 2 ~,~ n = ? $$ | 1 |
| 9280 | $$ a_1 = 1 ~,~ r = 2 ~,~ S_n = 16 ~,~ n = ? $$ | 1 |
| 9281 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 48 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $. | 1 |
| 9282 | Find $ a_10 $ of a geometric progression if $ a_1 = 48000 ~~ \text{and} ~~ r = 1.05 $. | 1 |
| 9283 | Find $ a_2 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 9284 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 8 } = 512 ~~ \text{and} ~~ a_{ 3 } = 16 $. | 1 |
| 9285 | $$ a_1 = \frac{ 8 }{ 3 } ~,~ r = \frac{ 3 }{ 2 } ~,~ S_n = 2500 ~,~ n = ? $$ | 1 |
| 9286 | Find $ a_9 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 9287 | Find $ a_6 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 9288 | Find $ a_3 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 9289 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9290 | Find $ a_9 $ of a geometric progression if $ a_1 = 7300000000 ~~ \text{and} ~~ r = 1.012 $. | 1 |
| 9291 | Find $ a_6 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 4 $. | 1 |
| 9292 | Find $ a_6 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $. | 1 |
| 9293 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 9294 | Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $. | 1 |
| 9295 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 384 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $. | 1 |
| 9296 | Find $ a_24 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = 48 $. | 1 |
| 9297 | Find $ a_7 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $. | 1 |
| 9298 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 2 ~~ \text{and} ~~ a_{ 5 } = \frac{ 1 }{ 4 } $. | 1 |
| 9299 | Find $ a_6 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $. | 1 |
| 9300 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ a_{ 3 } = 8 $. | 1 |
