Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 4751 | Find $ a_2 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 103 }{ 100 } $. | 2 |
| 4752 | Find $ a_4 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $. | 2 |
| 4753 | Find $ a_5 $ of a geometric progression if $ a_1 = 863.4 ~~ \text{and} ~~ r = 1.796 $. | 2 |
| 4754 | Find $ a_11 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = 2 $. | 2 |
| 4755 | Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -6 $. | 2 |
| 4756 | Find $ a_9 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 2 |
| 4757 | Find $ a_8 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 5 } $. | 2 |
| 4758 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $. | 2 |
| 4759 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $. | 2 |
| 4760 | Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $. | 2 |
| 4761 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $. | 2 |
| 4762 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $. | 2 |
| 4763 | Find $ a_6 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = 6 $. | 2 |
| 4764 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -7 ~~ \text{and} ~~ r = 6 $. | 2 |
| 4765 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 2 |
| 4766 | Find $ a_24 $ of a geometric progression if $ a_1 = 18875 ~~ \text{and} ~~ r = 1.116 $. | 2 |
| 4767 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 7 ~~ \text{and} ~~ a_{ 3 } = 567 $. | 2 |
| 4768 | Find $ a_10 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 4769 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 2 |
| 4770 | Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 4 $. | 2 |
| 4771 | Find $ a_4 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $. | 2 |
| 4772 | Find $ a_43 $ of a geometric progression if $ a_1 = 900 ~~ \text{and} ~~ r = 0.85 $. | 2 |
| 4773 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 4774 | Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 4775 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 600 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 2 |
| 4776 | Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 2 |
| 4777 | $$ a_1 = 2 ~,~ r = 0.25 ~,~ a_n = 9 ~,~ n = ? $$ | 2 |
| 4778 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 2 |
| 4779 | Find $ a_2 $ of a geometric progression if $ a_1 = 162 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 4780 | Find $ a_3 $ of a geometric progression if $ a_1 = 162 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 4781 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 9 } = 2187 ~~ \text{and} ~~ a_{ 20 } = \frac{ 1 }{ 81 } $. | 2 |
| 4782 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 14348907 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 2 |
| 4783 | Find $ a_12 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 2 |
| 4784 | $$ a_1 = 100 ~,~ r = \frac{ 4 }{ 5 } ~,~ a_n = 12 ~,~ n = ? $$ | 2 |
| 4785 | Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 2 |
| 4786 | $$ a_1 = 1 ~~,~~ r = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 2 |
| 4787 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -2 $. | 2 |
| 4788 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 9 }{ 10 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $. | 2 |
| 4789 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 8 }{ 125 } $. | 2 |
| 4790 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 28 ~~ \text{and} ~~ a_{ 448 } = 28 $. | 2 |
| 4791 | $$ a_1 = 3 ~,~ r = 2 ~,~ a_n = 3072 ~,~ n = ? $$ | 2 |
| 4792 | Find $ a_6 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 4793 | Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 2 $. | 2 |
| 4794 | Find $ a_10 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 81 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 4795 | Find $ a_10 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 81 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 2 |
| 4796 | Find $ a_5 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 4797 | Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 2 |
| 4798 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 2 |
| 4799 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 4800 | Find the sum of the first $ 46875 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $. | 2 |
