Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 9551 | Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 9552 | Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 1 |
| 9553 | Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9554 | Find the sum of the first $ 22 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9555 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 50 } $. | 1 |
| 9556 | Find $ a_5 $ of a geometric progression if $ a_1 = 21 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $. | 1 |
| 9557 | Find $ a_15 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $. | 1 |
| 9558 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 10 }{ 33 } ~~ \text{and} ~~ r = 2.012 $. | 1 |
| 9559 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 10 }{ 33 } ~~ \text{and} ~~ r = 2.012 $. | 1 |
| 9560 | Find $ a_7 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9561 | Find $ a_20 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 9562 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = \frac{ 36 }{ 7 } ~~ \text{and} ~~ r = \frac{ 2 }{ 7 } $. | 1 |
| 9563 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 9564 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.3544 $. | 1 |
| 9565 | Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 4 $. | 1 |
| 9566 | $$ a_1 = 10 ~,~ r = 1.01 ~,~ S_n = 382.6 ~,~ n = ? $$ | 1 |
| 9567 | $$ a_1 = 10 ~,~ r = 1.01 ~,~ S_n = 382.6 ~,~ n = ? $$ | 1 |
| 9568 | $$ a_1 = 10 ~,~ r = 1.01 ~,~ S_n = 243.1 ~,~ n = ? $$ | 1 |
| 9569 | $$ a_1 = 10 ~,~ r = 1.01 ~,~ S_n = 243.1 ~,~ n = ? $$ | 1 |
| 9570 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $. | 1 |
| 9571 | Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 7 $. | 1 |
| 9572 | Find $ a_8 $ of a geometric progression if $ a_1 = 26 ~~ \text{and} ~~ r = 5 $. | 1 |
| 9573 | Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -1.667 $. | 1 |
| 9574 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 5 }{ 4 } $. | 1 |
| 9575 | Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 3 } $. | 1 |
| 9576 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -\frac{ 5 }{ 3 } $. | 1 |
| 9577 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -7 ~~ \text{and} ~~ r = -\frac{ 5 }{ 3 } $. | 1 |
| 9578 | Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 9579 | Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 9580 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 9581 | Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 9582 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 131 ~~ \text{and} ~~ a_{ 6 } = 750 $. | 1 |
| 9583 | $$ a_1 = 1 ~,~ r = 2 ~,~ S_n = 10 ~,~ n = ? $$ | 1 |
| 9584 | Find $ a_2 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 1 $. | 1 |
| 9585 | Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $. | 1 |
| 9586 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $. | 1 |
| 9587 | Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $. | 1 |
| 9588 | Find $ a_11 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 9589 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 175 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 9590 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 150 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 1 |
| 9591 | Find $ a_5 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 9592 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 9593 | Find $ a_12 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -2 $. | 1 |
| 9594 | Find the sum of the first $ 9223372036854775807 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.09091 $. | 1 |
| 9595 | Find $ a_5 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -4 $. | 1 |
| 9596 | Find $ a_3 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 5 } $. | 1 |
| 9597 | Find $ a_2 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $. | 1 |
| 9598 | Find $ a_6 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 4 $. | 1 |
| 9599 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 250 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 9600 | Find $ a_7 $ of a geometric progression if $ a_1 = 250 ~~ \text{and} ~~ r = 1.25 $. | 1 |
