Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 10851 | Find $ a_10 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 4 $. | 1 |
| 10852 | Find $ a_9 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 4 $. | 1 |
| 10853 | Find $ a_11 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10854 | Find $ a_11 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = -4 $. | 1 |
| 10855 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 6 $. | 1 |
| 10856 | Find $ a_4 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10857 | Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 6 $. | 1 |
| 10858 | Find $ a_3 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 10859 | Find $ a_4 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 10860 | Find $ a_5 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 10861 | Find $ a_6 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 1 |
| 10862 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 6 } = 750 ~~ \text{and} ~~ a_{ 10 } = 3200 $. | 1 |
| 10863 | $$ a_1 = 324 ~~,~~ r = 3 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 10864 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 4 } = 324 $. | 1 |
| 10865 | Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -5 $. | 1 |
| 10866 | Find $ a_4 $ of a geometric progression if $ a_1 = 372 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 10867 | Find $ a_4 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -8 $. | 1 |
| 10868 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 23 }{ 100 } ~~ \text{and} ~~ r = 3 $. | 1 |
| 10869 | Find $ a_5 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -6 $. | 1 |
| 10870 | Find $ a_4 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -1 $. | 1 |
| 10871 | Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 8 $. | 1 |
| 10872 | Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -8 $. | 1 |
| 10873 | Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $. | 1 |
| 10874 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 77 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 77 } $. | 1 |
| 10875 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 77 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 77 } $. | 1 |
| 10876 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 6 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 10877 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $. | 1 |
| 10878 | Find $ a_3 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $. | 1 |
| 10879 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 3 ~~ \text{and} ~~ a_{ 5 } = \frac{ 3 }{ 64 } $. | 1 |
| 10880 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 4 } = \frac{ 112 }{ 5 } ~~ \text{and} ~~ a_{ 8 } = \frac{ 243 }{ 10 } $. | 1 |
| 10881 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 10882 | Find $ a_10 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 10883 | Find $ a_4 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 10884 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = -3 $. | 1 |
| 10885 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $. | 1 |
| 10886 | $$ a_1 = 4 ~,~ r = \frac{ 1 }{ 5 } ~,~ a_n = 2 ~,~ n = ? $$ | 1 |
| 10887 | Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 1 |
| 10888 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 2 } ~~ \text{and} ~~ r = -2 $. | 1 |
| 10889 | Find $ a_7 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $. | 1 |
| 10890 | Find $ a_7 $ of a geometric progression if $ a_1 = 153 ~~ \text{and} ~~ r = 5 $. | 1 |
| 10891 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 4 } = 162 $. | 1 |
| 10892 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 3 }{ 2 } ~~ \text{and} ~~ a_{ 3 } = 270 $. | 1 |
| 10893 | Find $ a_7 $ of a geometric progression if $ a_1 = 120 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 1 |
| 10894 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.384 $. | 1 |
| 10895 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 1 |
| 10896 | $$ a_1 = 4 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = \frac{ 1 }{ 16 } ~,~ n = ? $$ | 1 |
| 10897 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 10898 | $$ a_1 = 2 ~,~ r = 2 ~,~ a_n = 512 ~,~ n = ? $$ | 1 |
| 10899 | Find the sum of the first $ 48 $ terms of a geometric sequence if $ a_1 = 3657 ~~ \text{and} ~~ r = 6.9 $. | 1 |
| 10900 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
