Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 8301 | Find $ a_2 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8302 | Find $ a_1 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8303 | Find $ a_1 $ of a geometric progression if $ a_1 = 70 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 8304 | Find $ a_2 $ of a geometric progression if $ a_1 = 70 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 8305 | Find $ a_3 $ of a geometric progression if $ a_1 = 70 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 8306 | Find $ a_4 $ of a geometric progression if $ a_1 = 70 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 8307 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 0.04371 ~~ \text{and} ~~ r = 1.1 $. | 1 |
| 8308 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = -3 ~~ \text{and} ~~ a_{ 5 } = 244 $. | 1 |
| 8309 | Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -3 $. | 1 |
| 8310 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $. | 1 |
| 8311 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 4 } = 4 ~~ \text{and} ~~ a_{ 7 } = 12 $. | 1 |
| 8312 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8313 | Find $ a_11 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8314 | Find $ a_13 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -5 $. | 1 |
| 8315 | Find $ a_12 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 8316 | Find $ a_11 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8317 | Find $ a_6 $ of a geometric progression if $ a_1 = 243 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 1 |
| 8318 | $$ a_1 = 3 ~,~ r = 3 ~,~ a_n = 6561 ~,~ n = ? $$ | 1 |
| 8319 | Find $ a_7 $ of a geometric progression if $ a_1 = 3183 ~~ \text{and} ~~ r = 1 $. | 1 |
| 8320 | $$ a_1 = 46 ~,~ r = 1.003 ~,~ a_n = 15 ~,~ n = ? $$ | 1 |
| 8321 | Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 1.5 $. | 1 |
| 8322 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8323 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 800 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 8324 | Find $ a_4 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $. | 1 |
| 8325 | Find $ a_5 $ of a geometric progression if $ a_1 = -192 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 8326 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 2 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 8327 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = -3 $. | 1 |
| 8328 | $$ a_1 = 8 ~,~ r = 2 ~,~ a_n = 512 ~,~ n = ? $$ | 1 |
| 8329 | $$ a_1 = 8 ~,~ r = 8 ~,~ a_n = 13436928 ~,~ n = ? $$ | 1 |
| 8330 | $$ a_1 = 5 ~,~ r = 4 ~,~ a_n = 83886080 ~,~ n = ? $$ | 1 |
| 8331 | Find $ a_6 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8332 | Find $ a_25 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 8333 | Find $ a_100 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 8334 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6230 ~~ \text{and} ~~ r = 1.095 $. | 1 |
| 8335 | Find $ a_20 $ of a geometric progression if $ a_1 = 19613 ~~ \text{and} ~~ r = 1.06 $. | 1 |
| 8336 | $$ a_1 = 3 ~,~ r = 3 ~,~ S_n = 88572 ~,~ n = ? $$ | 1 |
| 8337 | Find $ a_8 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8338 | Find $ a_36 $ of a geometric progression if $ a_1 = 250 ~~ \text{and} ~~ r = 1.002 $. | 1 |
| 8339 | Find the sum of the first $ 100000000 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $. | 1 |
| 8340 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 6 $. | 1 |
| 8341 | Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.005 ~~ \text{and} ~~ r = 1.15 $. | 1 |
| 8342 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 6 $. | 1 |
| 8343 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 6 $. | 1 |
| 8344 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 495000 ~~ \text{and} ~~ r = 0.9 $. | 1 |
| 8345 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 495000 ~~ \text{and} ~~ r = 0.9 $. | 1 |
| 8346 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 495000 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $. | 1 |
| 8347 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 495000 ~~ \text{and} ~~ r = 0.9 $. | 1 |
| 8348 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 495000 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $. | 1 |
| 8349 | Find $ a_8 $ of a geometric progression if $ a_1 = -810 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8350 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -810 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
