Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 3901 | Find $ a_8 $ of a geometric progression if $ a_1 = 3280 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3902 | Find $ a_9 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 3903 | Find $ a_12 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3904 | Find $ a_4 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $. | 2 |
| 3905 | Find $ a_4 $ of a geometric progression if $ a_1 = 170 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 2 |
| 3906 | Find $ a_11 $ of a geometric progression if $ a_1 = 39000 ~~ \text{and} ~~ r = 0.5 $. | 2 |
| 3907 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 39000 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 3908 | Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 4 } $. | 2 |
| 3909 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 187345 ~~ \text{and} ~~ r = 0.02 $. | 2 |
| 3910 | Find $ a_10 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 2 |
| 3911 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 2 |
| 3912 | Find $ a_3 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = -8 $. | 2 |
| 3913 | Find $ a_10 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $. | 2 |
| 3914 | $$ a_1 = 1 ~,~ r = \frac{ 1 }{ 5 } ~,~ a_n = \frac{ 1 }{ 3125 } ~,~ n = ? $$ | 2 |
| 3915 | $$ a_1 = \frac{ 1 }{ 3 } ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = \frac{ 1 }{ 48 } ~,~ n = ? $$ | 2 |
| 3916 | Find $ a_1 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3917 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3918 | Find $ a_3 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -5 $. | 2 |
| 3919 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 729 ~~ \text{and} ~~ r = -3 $. | 2 |
| 3920 | Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 2 |
| 3921 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 2 |
| 3922 | Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 2 |
| 3923 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $. | 2 |
| 3924 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3925 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 2 ~~ \text{and} ~~ a_{ 4 } = 32 $. | 2 |
| 3926 | Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 8 $. | 2 |
| 3927 | Find $ a_9 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3928 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 5 }{ 3 } $. | 2 |
| 3929 | Find $ a_11 $ of a geometric progression if $ a_1 = 192 ~~ \text{and} ~~ r = 4 $. | 2 |
| 3930 | Find $ a_3 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $. | 2 |
| 3931 | Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $. | 2 |
| 3932 | Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -5 $. | 2 |
| 3933 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 48 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 3934 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 2 |
| 3935 | Find $ a_4 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3936 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 72 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3937 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 72 ~~ \text{and} ~~ r = \frac{ 3 }{ 10 } $. | 2 |
| 3938 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 10 } ~~ \text{and} ~~ r = 2 $. | 2 |
| 3939 | Find $ a_11 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -4 $. | 2 |
| 3940 | $$ a_1 = 7 ~,~ r = 2 ~,~ a_n = 3584 ~,~ n = ? $$ | 2 |
| 3941 | $$ a_1 = 2 ~,~ r = 2 ~,~ a_n = 7 ~,~ n = ? $$ | 2 |
| 3942 | $$ a_1 = 2 ~,~ r = 2 ~,~ S_n = 126 ~,~ n = ? $$ | 2 |
| 3943 | Find $ a_8 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 2 |
| 3944 | Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 10 } ~~ \text{and} ~~ r = 10 $. | 2 |
| 3945 | Find $ a_20 $ of a geometric progression if $ a_1 = \dfrac{ 45 }{ 16 } ~~ \text{and} ~~ r = 2 $. | 2 |
| 3946 | Find $ a_6 $ of a geometric progression if $ a_1 = -192 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 2 |
| 3947 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 11 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3948 | Find $ a_2 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 5 $. | 2 |
| 3949 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $. | 2 |
| 3950 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 2 |
