Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 8901 | Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 8902 | Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8903 | $$ a_1 = 6 ~,~ r = 8 ~,~ S_n = 805306368 ~,~ n = ? $$ | 1 |
| 8904 | Find $ a_100 $ of a geometric progression if $ a_1 = 1.0E-14 ~~ \text{and} ~~ r = 1.15 $. | 1 |
| 8905 | Find $ a_101 $ of a geometric progression if $ a_1 = 1.0E-14 ~~ \text{and} ~~ r = 1.15 $. | 1 |
| 8906 | Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $. | 1 |
| 8907 | Find $ a_5 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -7 $. | 1 |
| 8908 | Find $ a_9 $ of a geometric progression if $ a_1 = 13122 ~~ \text{and} ~~ r = -4 $. | 1 |
| 8909 | Find $ a_9 $ of a geometric progression if $ a_1 = 13122 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8910 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $. | 1 |
| 8911 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $. | 1 |
| 8912 | Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 1 |
| 8913 | Find $ a_5 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $. | 1 |
| 8914 | Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $. | 1 |
| 8915 | Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8916 | Find $ a_10 $ of a geometric progression if $ a_1 = 1600 ~~ \text{and} ~~ r = 0.125 $. | 1 |
| 8917 | Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 8918 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 1 }{ 3 } ~~ \text{and} ~~ a_{ 5 } = 243 $. | 1 |
| 8919 | Find $ a_3 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8920 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 4 } = 5.184 $. | 1 |
| 8921 | Find $ a_2 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8922 | Find $ a_7 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8923 | Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $. | 1 |
| 8924 | Find $ a_8 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -16 $. | 1 |
| 8925 | Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8926 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8927 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 1 |
| 8928 | Find $ a_14 $ of a geometric progression if $ a_1 = 19 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 1 |
| 8929 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 19 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 8930 | Find $ a_5 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -1 $. | 1 |
| 8931 | Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8932 | Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $. | 1 |
| 8933 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 24 ~~ \text{and} ~~ r = 0.7 $. | 1 |
| 8934 | Find $ a_12 $ of a geometric progression if $ a_1 = 4096 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 1 |
| 8935 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 32 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8936 | Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $. | 1 |
| 8937 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 16 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 8938 | $$ a_1 = 3 ~,~ r = 3 ~,~ a_n = 27 ~,~ n = ? $$ | 1 |
| 8939 | $$ a_1 = 2 ~,~ r = 3 ~,~ a_n = 18 ~,~ n = ? $$ | 1 |
| 8940 | $$ a_1 = 25 ~,~ r = 7 ~,~ a_n = 8575 ~,~ n = ? $$ | 1 |
| 8941 | Find $ a_4 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 6 $. | 1 |
| 8942 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 70000 ~~ \text{and} ~~ r = -\frac{ 21 }{ 20 } $. | 1 |
| 8943 | $$ a_1 = 8 ~,~ r = 2 ~,~ a_n = 524288 ~,~ n = ? $$ | 1 |
| 8944 | Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8945 | Find $ a_11 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $. | 1 |
| 8946 | Find $ a_2 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 8947 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 175 ~~ \text{and} ~~ r = -\frac{ 5 }{ 2 } $. | 1 |
| 8948 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 1 }{ 64 } ~~ \text{and} ~~ a_{ 3 } = \frac{ 1 }{ 16 } $. | 1 |
| 8949 | Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 64 } ~~ \text{and} ~~ r = 2 $. | 1 |
| 8950 | Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 64 } ~~ \text{and} ~~ r = -2 $. | 1 |
