Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 3301 | Find $ a_11 $ of a geometric progression if $ a_1 = \dfrac{ 704 }{ 81 } ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $. | 2 |
| 3302 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $. | 2 |
| 3303 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3304 | Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 2 |
| 3305 | Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 3306 | Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 2 |
| 3307 | Find $ a_3 $ of a geometric progression if $ a_1 = 21 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 3308 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3309 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 2 |
| 3310 | Find $ a_7 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $. | 2 |
| 3311 | Find $ a_15 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 6 } ~~ \text{and} ~~ r = 3 $. | 2 |
| 3312 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $. | 2 |
| 3313 | Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 2 |
| 3314 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -48 ~~ \text{and} ~~ r = -4 $. | 2 |
| 3315 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -48 ~~ \text{and} ~~ r = -4 $. | 2 |
| 3316 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -48 ~~ \text{and} ~~ r = -2 $. | 2 |
| 3317 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -48 ~~ \text{and} ~~ r = -2 $. | 2 |
| 3318 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -48 ~~ \text{and} ~~ r = -2 $. | 2 |
| 3319 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -48 ~~ \text{and} ~~ r = -2 $. | 2 |
| 3320 | Find the sum of the first $ 210 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.1 $. | 2 |
| 3321 | Find the sum of the first $ 400 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 0.999 $. | 2 |
| 3322 | Find $ a_10 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 6 $. | 2 |
| 3323 | Find $ a_5 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 6 $. | 2 |
| 3324 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 3325 | Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 2 |
| 3326 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 2 |
| 3327 | Find $ a_16 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 8 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 3328 | Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3329 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 16 } = 1 ~~ \text{and} ~~ a_{ 4 } = 2 $. | 2 |
| 3330 | Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 3331 | $$ a_1 = 14 ~~,~~ r = 3 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 2 |
| 3332 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 48 } ~~ \text{and} ~~ r = -4 $. | 2 |
| 3333 | Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = -5 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 2 |
| 3334 | Find the sum of the first $ 56 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $. | 2 |
| 3335 | Find $ a_10 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 3336 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 26 ~~ \text{and} ~~ r = -5 $. | 2 |
| 3337 | $$ a_1 = 2 ~,~ r = 3 ~,~ a_n = 28697814 ~,~ n = ? $$ | 2 |
| 3338 | Find $ a_2 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3339 | Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -2 $. | 2 |
| 3340 | Find $ a_6 $ of a geometric progression if $ a_1 = 3000 ~~ \text{and} ~~ r = -1 $. | 2 |
| 3341 | Find $ a_18 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $. | 2 |
| 3342 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 2 |
| 3343 | Find $ a_5 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 9 } $. | 2 |
| 3344 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = 3 $. | 2 |
| 3345 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3346 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 16 } ~~ \text{and} ~~ r = 1.5 $. | 2 |
| 3347 | $$ a_1 = 12 ~,~ r = 3 ~,~ a_n = 324 ~,~ n = ? $$ | 2 |
| 3348 | Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 1.05 $. | 2 |
| 3349 | $$ a_1 = 5 ~,~ r = 2 ~,~ a_n = 81920 ~,~ n = ? $$ | 2 |
| 3350 | Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 2 |
