Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 3701 | $$ a_1 = 2 ~~,~~ r = \frac{ 1 }{ 3 } ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 2 |
| 3702 | Find $ a_10 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -3 $. | 2 |
| 3703 | Find $ a_9 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 4 $. | 2 |
| 3704 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3705 | $$ a_1 = 9 ~,~ r = \frac{ 28 }{ 25 } ~,~ a_n = 15 ~,~ n = ? $$ | 2 |
| 3706 | Find $ a_15 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3707 | Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.08 $. | 2 |
| 3708 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.08 $. | 2 |
| 3709 | Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $. | 2 |
| 3710 | Find $ a_11 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $. | 2 |
| 3711 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 2 } = 5.828 ~~ \text{and} ~~ a_{ 3 } = 25.73 $. | 2 |
| 3712 | Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 2 } $. | 2 |
| 3713 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 5 }{ 9 } $. | 2 |
| 3714 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 2 |
| 3715 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 2 |
| 3716 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 2 |
| 3717 | Find $ a_10 $ of a geometric progression if $ a_1 = 58 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3718 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $. | 2 |
| 3719 | Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 19 ~~ \text{and} ~~ r = \frac{ 2 }{ 7 } $. | 2 |
| 3720 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3721 | Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3722 | Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3723 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -\frac{ 3 }{ 8 } ~~ \text{and} ~~ r = 2 $. | 2 |
| 3724 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $. | 2 |
| 3725 | Find $ a_5 $ of a geometric progression if $ a_1 = -128 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $. | 2 |
| 3726 | Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 9 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 2 |
| 3727 | Find the sum of the first $ 120 $ terms of a geometric sequence if $ a_1 = 4000 ~~ \text{and} ~~ r = 1.004 $. | 2 |
| 3728 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3729 | Find $ a_100 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 0.001 $. | 2 |
| 3730 | $$ a_1 = 180000 ~,~ r = \frac{ 1 }{ 25 } ~,~ a_n = 22 ~,~ n = ? $$ | 2 |
| 3731 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = 1 $. | 2 |
| 3732 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.96 $. | 2 |
| 3733 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $. | 2 |
| 3734 | Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $. | 2 |
| 3735 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = 2 $. | 2 |
| 3736 | Find $ a_5 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 3737 | Find $ a_4 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 2 |
| 3738 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $. | 2 |
| 3739 | Find $ a_4 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 2 |
| 3740 | Find $ a_368 $ of a geometric progression if $ a_1 = 1.0E-6 ~~ \text{and} ~~ r = 1.1 $. | 2 |
| 3741 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 3 $. | 2 |
| 3742 | Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 1 $. | 2 |
| 3743 | Find $ a_13 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 2 |
| 3744 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 25 ~~ \text{and} ~~ r = \frac{ 16 }{ 25 } $. | 2 |
| 3745 | Find $ a_3 $ of a geometric progression if $ a_1 = 35 ~~ \text{and} ~~ r = 12 $. | 2 |
| 3746 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $. | 2 |
| 3747 | Find $ a_100 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 2 |
| 3748 | Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $. | 2 |
| 3749 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $. | 2 |
| 3750 | $$ a_1 = 22000000000 ~,~ r = \frac{ 49 }{ 50 } ~,~ a_n = 1 ~,~ n = ? $$ | 2 |
