Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 7351 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 7352 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = 1 $. | 1 |
| 7353 | Find $ a_1 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 7354 | Find $ a_1 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 1 |
| 7355 | Find the sum of the first $ 22 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 7356 | Find the sum of the first $ 22 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 7357 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 7358 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 50000 ~~ \text{and} ~~ r = \frac{ 26 }{ 25 } $. | 1 |
| 7359 | Find $ a_3 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = \dfrac{ 26 }{ 25 } $. | 1 |
| 7360 | Find $ a_9 $ of a geometric progression if $ a_1 = 66 ~~ \text{and} ~~ r = 2 $. | 1 |
| 7361 | Find $ a_6 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -3 $. | 1 |
| 7362 | Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -6 $. | 1 |
| 7363 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 640 ~~ \text{and} ~~ r = 100 $. | 1 |
| 7364 | Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -5 $. | 1 |
| 7365 | Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 2 } $. | 1 |
| 7366 | Find $ a_5 $ of a geometric progression if $ a_1 = 4000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 7367 | Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 7368 | Find $ a_6 $ of a geometric progression if $ a_1 = 610.9 ~~ \text{and} ~~ r = 1.871 $. | 1 |
| 7369 | Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 7370 | Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 36 $. | 1 |
| 7371 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 7372 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 18000 ~~ \text{and} ~~ r = -\frac{ 3 }{ 20 } $. | 1 |
| 7373 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 50000 ~~ \text{and} ~~ r = \frac{ 1 }{ 25 } $. | 1 |
| 7374 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 7375 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $. | 1 |
| 7376 | Find $ a_12 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 3 $. | 1 |
| 7377 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 4 }{ 3 } $. | 1 |
| 7378 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 1 } = 10 ~~ \text{and} ~~ a_{ 3 } = \frac{ 32 }{ 5 } $. | 1 |
| 7379 | Find the sum of the first $ 42 $ terms of a geometric sequence if $ a_1 = 84 ~~ \text{and} ~~ r = -0.95 $. | 1 |
| 7380 | Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -4 $. | 1 |
| 7381 | Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -3 $. | 1 |
| 7382 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 7383 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 0.25 ~~ \text{and} ~~ r = 0.75 $. | 1 |
| 7384 | Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 0.999 $. | 1 |
| 7385 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = -\frac{ 7 }{ 20 } $. | 1 |
| 7386 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 7 }{ 20 } $. | 1 |
| 7387 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 9 }{ 10 } $. | 1 |
| 7388 | Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 9 }{ 10 } $. | 1 |
| 7389 | Find the sum of the first $ 1000 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 7390 | Find $ a_7 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 7391 | Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 8 } $. | 1 |
| 7392 | Find $ a_8 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 3 $. | 1 |
| 7393 | $$ a_1 = 1000 ~~,~~ r = \frac{ 1 }{ 5 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 7394 | $$ a_1 = -48 ~~,~~ r = -\frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 7395 | Find $ a_10 $ of a geometric progression if $ a_1 = -48 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 7396 | Find $ a_20 $ of a geometric progression if $ a_1 = -48 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 7397 | $$ a_1 = 6 ~,~ r = 5 ~,~ a_n = 100000 ~,~ n = ? $$ | 1 |
| 7398 | $$ a_1 = 6 ~,~ r = 5 ~,~ a_n = 10000 ~,~ n = ? $$ | 1 |
| 7399 | Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 5 $. | 1 |
| 7400 | Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 5 $. | 1 |
