Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 6351 | Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $. | 2 |
| 6352 | Find $ a_3 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 21 }{ 20 } $. | 2 |
| 6353 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $. | 2 |
| 6354 | Find $ a_3 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.05 $. | 2 |
| 6355 | Find $ a_8 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = 1.06 $. | 2 |
| 6356 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ r = -5 $. | 2 |
| 6357 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0.8 ~~ \text{and} ~~ r = -5 $. | 2 |
| 6358 | Find $ a_12 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 6359 | Find $ a_16 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $. | 2 |
| 6360 | Find $ a_99999 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 9 } $. | 2 |
| 6361 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 5 } ~~ \text{and} ~~ r = 5 $. | 2 |
| 6362 | Find $ a_6 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 4 } $. | 2 |
| 6363 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 6364 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2400 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 2 |
| 6365 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $. | 2 |
| 6366 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 2 |
| 6367 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 6368 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $. | 2 |
| 6369 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 2 |
| 6370 | Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $. | 2 |
| 6371 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 5 }{ 2 } $. | 2 |
| 6372 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 200000 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 2 |
| 6373 | Find $ a_4 $ of a geometric progression if $ a_1 = 200000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 2 |
| 6374 | Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 1 $. | 2 |
| 6375 | Find $ a_2 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = \dfrac{ 17 }{ 20 } $. | 2 |
| 6376 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 6 } = 250 ~~ \text{and} ~~ a_{ 3 } = 16 $. | 2 |
| 6377 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 1 } = 64 ~~ \text{and} ~~ a_{ 2 } = 36 $. | 2 |
| 6378 | $$ a_1 = 1 ~,~ r = 9 ~,~ S_n = 7381 ~,~ n = ? $$ | 2 |
| 6379 | $$ a_1 = 7 ~,~ r = 3 ~,~ a_n = 1701 ~,~ n = ? $$ | 2 |
| 6380 | Find $ a_4 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = -3 $. | 2 |
| 6381 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4096 ~~ \text{and} ~~ r = -\frac{ 1 }{ 8 } $. | 2 |
| 6382 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 42 ~~ \text{and} ~~ r = \frac{ 19 }{ 20 } $. | 2 |
| 6383 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 2 |
| 6384 | Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 16 }{ 5 } $. | 2 |
| 6385 | Find $ a_5 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 6386 | Find $ a_1 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 199 }{ 100 } $. | 2 |
| 6387 | $$ a_1 = 50 ~,~ r = 1.99 ~,~ a_n = 49.5 ~,~ n = ? $$ | 2 |
| 6388 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 5 } = 12 ~~ \text{and} ~~ a_{ 8 } = \frac{ 256 }{ 9 } $. | 2 |
| 6389 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 3 $. | 2 |
| 6390 | Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -6 $. | 2 |
| 6391 | Find $ a_12 $ of a geometric progression if $ a_1 = 15400 ~~ \text{and} ~~ r = 1.035 $. | 2 |
| 6392 | $$ a_1 = 40 ~,~ r = \frac{ 1 }{ 3 } ~,~ S_n = 60 ~,~ n = ? $$ | 2 |
| 6393 | $$ a_1 = 40 ~,~ r = \frac{ 1 }{ 3 } ~,~ S_n = 58 ~,~ n = ? $$ | 2 |
| 6394 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 10 } ~~ \text{and} ~~ r = 1 $. | 2 |
| 6395 | $$ a_1 = \frac{ 1 }{ 10 } ~~,~~ r = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 2 |
| 6396 | Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -14 $. | 2 |
| 6397 | Find $ a_5 $ of a geometric progression if $ a_1 = -14 ~~ \text{and} ~~ r = 2 $. | 2 |
| 6398 | Find $ a_2 $ of a geometric progression if $ a_1 = 97390 ~~ \text{and} ~~ r = 1.025 $. | 2 |
| 6399 | Find $ a_2 $ of a geometric progression if $ a_1 = 625 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 2 |
| 6400 | Find $ a_5 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = 2 $. | 2 |
