Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 9901 | $$ a_1 = 4 ~,~ r = 5 ~,~ a_n = 8 ~,~ n = ? $$ | 1 |
| 9902 | Find $ a_9 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 6 } $. | 1 |
| 9903 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -7 ~~ \text{and} ~~ r = -\frac{ 1 }{ 6 } $. | 1 |
| 9904 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 42 ~~ \text{and} ~~ r = -\frac{ 1 }{ 6 } $. | 1 |
| 9905 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 42 ~~ \text{and} ~~ r = -\frac{ 1 }{ 6 } $. | 1 |
| 9906 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 5 $. | 1 |
| 9907 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 9908 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 1 |
| 9909 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 1 |
| 9910 | Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 49 }{ 10 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 9911 | Find $ a_6 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = 2 $. | 1 |
| 9912 | Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 103 }{ 100 } ~~ \text{and} ~~ r = 5 $. | 1 |
| 9913 | Find $ a_5 $ of a geometric progression if $ a_1 = -13 ~~ \text{and} ~~ r = -2 $. | 1 |
| 9914 | Find $ a_6 $ of a geometric progression if $ a_1 = 41 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 1 |
| 9915 | Find $ a_6 $ of a geometric progression if $ a_1 = 679 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 9916 | Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 1 |
| 9917 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $. | 1 |
| 9918 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 25 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $. | 1 |
| 9919 | Find $ a_4 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 1 |
| 9920 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 9921 | Find $ a_30 $ of a geometric progression if $ a_1 = 40000 ~~ \text{and} ~~ r = 1.033 $. | 1 |
| 9922 | Find $ a_10 $ of a geometric progression if $ a_1 = 45 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 9 } $. | 1 |
| 9923 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 1 |
| 9924 | Find $ a_10 $ of a geometric progression if $ a_1 = 100000 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $. | 1 |
| 9925 | Find $ a_50 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 7 $. | 1 |
| 9926 | Find $ a_7 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 6 $. | 1 |
| 9927 | Find $ a_10 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 6 $. | 1 |
| 9928 | Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $. | 1 |
| 9929 | Find $ a_7 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $. | 1 |
| 9930 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 70000 ~~ \text{and} ~~ r = 1.03 $. | 1 |
| 9931 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.14 $. | 1 |
| 9932 | Find the sum of the first $ 60 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.14 $. | 1 |
| 9933 | Find the sum of the first $ 60 $ terms of a geometric sequence if $ a_1 = 5000 ~~ \text{and} ~~ r = 1.02 $. | 1 |
| 9934 | Find $ a_6 $ of a geometric progression if $ a_1 = 0.375 ~~ \text{and} ~~ r = 8 $. | 1 |
| 9935 | Find $ a_6 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 9936 | Find $ a_5 $ of a geometric progression if $ a_1 = 1458 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 9937 | Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 5 $. | 1 |
| 9938 | Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 50.54 ~~ \text{and} ~~ r = 1.076 $. | 1 |
| 9939 | $$ a_1 = 100 ~~,~~ r = \frac{ 1 }{ 2 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 1 |
| 9940 | $$ a_1 = 80 ~,~ r = \frac{ 19 }{ 20 } ~,~ a_n = 10 ~,~ n = ? $$ | 1 |
| 9941 | $$ a_1 = 80 ~,~ r = 0.95 ~,~ a_n = 10 ~,~ n = ? $$ | 1 |
| 9942 | Find $ a_10 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 0.95 $. | 1 |
| 9943 | Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 4 } $. | 1 |
| 9944 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 2 ~~ \text{and} ~~ a_{ 9 } = 3577 $. | 1 |
| 9945 | $$ a_1 = 100 ~,~ r = \frac{ 27 }{ 25 } ~,~ a_n = 50 ~,~ n = ? $$ | 1 |
| 9946 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -3 $. | 1 |
| 9947 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -4 $. | 1 |
| 9948 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -6 $. | 1 |
| 9949 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $. | 1 |
| 9950 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 25000 ~~ \text{and} ~~ r = 0.0025 $. | 1 |
