Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 9801 | Find $ a_4 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = -22 $. | 1 |
| 9802 | Find $ a_2 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 8 } $. | 1 |
| 9803 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $. | 1 |
| 9804 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $. | 1 |
| 9805 | Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $. | 1 |
| 9806 | Find the sum of the first $ 24 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9807 | Find $ a_13 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9808 | Find $ a_9 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9809 | Find $ a_7 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9810 | Find $ a_3 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 9811 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 9812 | Find $ a_100 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.02 $. | 1 |
| 9813 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 15 ~~ \text{and} ~~ a_{ 3 } = 30 $. | 1 |
| 9814 | Find $ a_7 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = 4 $. | 1 |
| 9815 | Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9816 | $$ a_1 = 18 ~,~ r = \frac{ 2 }{ 3 } ~,~ a_n = \frac{ 512 }{ 729 } ~,~ n = ? $$ | 1 |
| 9817 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 850500 ~~ \text{and} ~~ a_{ 3 } = \frac{ 4424301 }{ 5 } $. | 1 |
| 9818 | Find $ a_15 $ of a geometric progression if $ a_1 = 850500 ~~ \text{and} ~~ r = 1.02 $. | 1 |
| 9819 | Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 9820 | Find $ a_15 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 9821 | Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 9822 | Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 9823 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 13 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 9824 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 5 } = 243 $. | 1 |
| 9825 | Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 9826 | Find $ a_13 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $. | 1 |
| 9827 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 26 } ~~ \text{and} ~~ r = \frac{ 25 }{ 26 } $. | 1 |
| 9828 | $$ a_1 = 83 ~,~ r = \frac{ 107 }{ 100 } ~,~ S_n = \frac{ 308163 }{ 20 } ~,~ n = ? $$ | 1 |
| 9829 | Find $ a_4 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9830 | Find $ a_7 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 7 $. | 1 |
| 9831 | Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $. | 1 |
| 9832 | Find $ a_5 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9833 | Find $ a_7 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 9834 | Find $ a_8 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -5 $. | 1 |
| 9835 | $$ a_1 = 1 ~,~ r = 3 ~,~ S_n = 182 ~,~ n = ? $$ | 1 |
| 9836 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $. | 1 |
| 9837 | Find $ a_14 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -3 $. | 1 |
| 9838 | Find $ a_1 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = \dfrac{ 19 }{ 5 } $. | 1 |
| 9839 | $$ a_1 = 9 ~,~ r = 6 ~,~ a_n = 15116544 ~,~ n = ? $$ | 1 |
| 9840 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 28 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $. | 1 |
| 9841 | Find $ a_31 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $. | 1 |
| 9842 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9843 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9844 | Find $ a_100 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $. | 1 |
| 9845 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 4 $. | 1 |
| 9846 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 3 $. | 1 |
| 9847 | Find $ a_5 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 9848 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 1 |
| 9849 | Find the sum of the first $ 80 $ terms of a geometric sequence if $ a_1 = 1.6 ~~ \text{and} ~~ r = 0.92 $. | 1 |
| 9850 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $. | 1 |
