Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 10701 | $$ a_1 = 6 ~~,~~ r = 7 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 10702 | Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10703 | Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10704 | Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10705 | Find $ a_3 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10706 | Find $ a_4 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10707 | Find $ a_8 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10708 | Find $ a_9 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10709 | Find $ a_10 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10710 | Find $ a_11 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10711 | Find $ a_30 $ of a geometric progression if $ a_1 = 175 ~~ \text{and} ~~ r = 2 $. | 1 |
| 10712 | Find $ a_16 $ of a geometric progression if $ a_1 = 0.0987 ~~ \text{and} ~~ r = 0.1975 $. | 1 |
| 10713 | Find $ a_4 $ of a geometric progression if $ a_1 = 0.0987 ~~ \text{and} ~~ r = 0.1975 $. | 1 |
| 10714 | Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 40 $. | 1 |
| 10715 | Find $ a_5 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 5 $. | 1 |
| 10716 | Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 10717 | Find $ a_2 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -5 $. | 1 |
| 10718 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 500 ~~ \text{and} ~~ r = 0.707 $. | 1 |
| 10719 | Find $ a_3 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 18 $. | 1 |
| 10720 | Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 5 $. | 1 |
| 10721 | Find $ a_16 $ of a geometric progression if $ a_1 = 24000 ~~ \text{and} ~~ r = 0.96 $. | 1 |
| 10722 | Find $ a_17 $ of a geometric progression if $ a_1 = 24000 ~~ \text{and} ~~ r = 0.96 $. | 1 |
| 10723 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = -3 $. | 1 |
| 10724 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 10725 | $$ a_1 = 1000000 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = 0.025 ~,~ n = ? $$ | 1 |
| 10726 | $$ a_1 = 1000000 ~,~ r = \frac{ 41 }{ 50 } ~,~ a_n = 0.025 ~,~ n = ? $$ | 1 |
| 10727 | $$ a_1 = 1000000 ~,~ r = 0.9904 ~,~ a_n = 0.025 ~,~ n = ? $$ | 1 |
| 10728 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 5 }{ 9 } $. | 1 |
| 10729 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $. | 1 |
| 10730 | Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $. | 1 |
| 10731 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = 7 $. | 1 |
| 10732 | $$ a_1 = 3 ~,~ r = 2 ~,~ a_n = 12288 ~,~ n = ? $$ | 1 |
| 10733 | Find $ a_6 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10734 | Find $ a_7 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 11 $. | 1 |
| 10735 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 10736 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $. | 1 |
| 10737 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 1 |
| 10738 | Find $ a_6 $ of a geometric progression if $ a_1 = 160 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 10739 | Find $ a_5 $ of a geometric progression if $ a_1 = 1200 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $. | 1 |
| 10740 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1200 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 10741 | Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 1200 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 10742 | Find the sum of the first $ 60 $ terms of a geometric sequence if $ a_1 = 1200 ~~ \text{and} ~~ r = 1.2 $. | 1 |
| 10743 | Find $ a_3 $ of a geometric progression if $ a_1 = 47800 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 2 } $. | 1 |
| 10744 | Find $ a_6 $ of a geometric progression if $ a_1 = 28900 ~~ \text{and} ~~ r = 7 $. | 1 |
| 10745 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10746 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $. | 1 |
| 10747 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $. | 1 |
| 10748 | Find $ a_2 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $. | 1 |
| 10749 | Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 1 $. | 1 |
| 10750 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
