Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 10301 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $. | 1 |
| 10302 | Find $ a_4 $ of a geometric progression if $ a_1 = 37000 ~~ \text{and} ~~ r = \dfrac{ 53 }{ 50 } $. | 1 |
| 10303 | Find $ a_4 $ of a geometric progression if $ a_1 = 45000 ~~ \text{and} ~~ r = \dfrac{ 107 }{ 100 } $. | 1 |
| 10304 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 10305 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 10306 | Find $ a_5 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = 12 $. | 1 |
| 10307 | Find $ a_4 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 10308 | Find $ a_368 $ of a geometric progression if $ a_1 = 1.0E-6 ~~ \text{and} ~~ r = 2 $. | 1 |
| 10309 | Find $ a_368 $ of a geometric progression if $ a_1 = 1.0E-8 ~~ \text{and} ~~ r = 2 $. | 1 |
| 10310 | Find $ a_2 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10311 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 3 }{ 2 } $. | 1 |
| 10312 | Find $ a_5 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 10313 | Find $ a_1 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = 4 $. | 1 |
| 10314 | Find $ a_4 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = 4 $. | 1 |
| 10315 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 27000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $. | 1 |
| 10316 | Find $ a_5 $ of a geometric progression if $ a_1 = 27000 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $. | 1 |
| 10317 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 1.3 $. | 1 |
| 10318 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 300 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $. | 1 |
| 10319 | Find $ a_5 $ of a geometric progression if $ a_1 = 1200 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $. | 1 |
| 10320 | Find $ a_100 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 10321 | Find $ a_50 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $. | 1 |
| 10322 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 900 ~~ \text{and} ~~ r = \frac{ 28 }{ 25 } $. | 1 |
| 10323 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -54 ~~ \text{and} ~~ r = -3 $. | 1 |
| 10324 | Find $ a_5 $ of a geometric progression if $ a_1 = -54 ~~ \text{and} ~~ r = -3 $. | 1 |
| 10325 | Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -6 $. | 1 |
| 10326 | Find $ a_9 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 10327 | $$ a_1 = 2200000000 ~,~ r = \frac{ 49 }{ 50 } ~,~ S_n = 100 ~,~ n = ? $$ | 1 |
| 10328 | $$ a_1 = 2200000000 ~,~ r = \frac{ 49 }{ 50 } ~,~ a_n = 100 ~,~ n = ? $$ | 1 |
| 10329 | $$ a_1 = 2200000000 ~,~ r = \frac{ 49 }{ 50 } ~,~ a_n = 1 ~,~ n = ? $$ | 1 |
| 10330 | $$ a_1 = 2200000000 ~,~ r = \frac{ 49 }{ 50 } ~,~ a_n = \frac{ 1 }{ 10 } ~,~ n = ? $$ | 1 |
| 10331 | Find $ a_5 $ of a geometric progression if $ a_1 = 26750 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 5 } $. | 1 |
| 10332 | Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10333 | Find $ a_7 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 5 $. | 1 |
| 10334 | Find $ a_5 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 2 $. | 1 |
| 10335 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 10336 | Find $ a_6 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = -3 $. | 1 |
| 10337 | Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 53 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $. | 1 |
| 10338 | Find $ a_19 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $. | 1 |
| 10339 | Find $ a_10 $ of a geometric progression if $ a_1 = 7300000000 ~~ \text{and} ~~ r = 1.017 $. | 1 |
| 10340 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10341 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $. | 1 |
| 10342 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = -2 $. | 1 |
| 10343 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 25 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 10344 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 1 |
| 10345 | $$ a_1 = 2 ~,~ r = 1.871 ~,~ a_n = 2 ~,~ n = ? $$ | 1 |
| 10346 | Find $ a_3 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 1 $. | 1 |
| 10347 | Find $ a_6 $ of a geometric progression if $ a_1 = 625 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $. | 1 |
| 10348 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 3 }{ 5 } ~~ \text{and} ~~ a_{ 6 } = \frac{ 243 }{ 5 } $. | 1 |
| 10349 | $$ a_1 = 625 ~,~ r = \frac{ 3 }{ 5 } ~,~ S_n = 225 ~,~ n = ? $$ | 1 |
| 10350 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
