Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 2001 | Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 4 |
| 2002 | Find $ a_13 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $. | 4 |
| 2003 | Find $ a_7 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $. | 4 |
| 2004 | Find $ a_16 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2005 | Find $ a_12 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2006 | Find $ a_8 $ of a geometric progression if $ a_1 = 2239488 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 4 |
| 2007 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2239488 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 4 |
| 2008 | Find $ a_7 $ of a geometric progression if $ a_1 = 960 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 4 |
| 2009 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $. | 4 |
| 2010 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $. | 4 |
| 2011 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 4 |
| 2012 | Find $ a_13 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2013 | Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 700 ~~ \text{and} ~~ r = 1.06 $. | 4 |
| 2014 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2015 | Find $ a_11 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 4 $. | 4 |
| 2016 | Find $ a_10 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2017 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 17 ~~ \text{and} ~~ r = 34 $. | 4 |
| 2018 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $. | 4 |
| 2019 | $$ a_1 = 50 ~,~ r = \frac{ 1 }{ 5 } ~,~ a_n = \frac{ 1 }{ 5 } ~,~ n = ? $$ | 4 |
| 2020 | Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2021 | Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2022 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2023 | Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 4 |
| 2024 | $$ a_1 = 2 ~,~ r = 2 ~,~ a_n = 1 ~,~ n = ? $$ | 4 |
| 2025 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $. | 4 |
| 2026 | Find the sum of the first $ 6000 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $. | 4 |
| 2027 | Find $ a_365 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2028 | Find $ a_5 $ of a geometric progression if $ a_1 = 84 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $. | 4 |
| 2029 | $$ a_1 = 4 ~,~ r = 3 ~,~ S_n = 4372 ~,~ n = ? $$ | 4 |
| 2030 | Find $ a_30 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 0.8 $. | 4 |
| 2031 | Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $. | 4 |
| 2032 | Find $ a_8 $ of a geometric progression if $ a_1 = 730 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $. | 4 |
| 2033 | Find $ a_8 $ of a geometric progression if $ a_1 = 730 ~~ \text{and} ~~ r = 1.009 $. | 4 |
| 2034 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $. | 4 |
| 2035 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $. | 4 |
| 2036 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 4 }{ 9 } $. | 4 |
| 2037 | Find $ a_10 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $. | 4 |
| 2038 | Find $ a_13 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $. | 4 |
| 2039 | Find $ a_5 $ of a geometric progression if $ a_1 = 578 ~~ \text{and} ~~ r = -7 $. | 4 |
| 2040 | Find $ a_256 $ of a geometric progression if $ a_1 = 625 ~~ \text{and} ~~ r = 1.24 $. | 4 |
| 2041 | Find first element ( $ a_1 $ ) and a common ration ( $ r $ )
of a geometic progression if $ a_{ 4 } = 5 ~~ \text{and} ~~ a_{ 8 } = 80 $. | 4 |
| 2042 | Find $ a_20 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $. | 4 |
| 2043 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 4 } = 720 $. | 4 |
| 2044 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = 2 ~~ \text{and} ~~ a_{ 8 } = 1530 $. | 4 |
| 2045 | $$ a_1 = \frac{ 2 }{ 3 } ~,~ r = \frac{ 5 }{ 2 } ~,~ S_n = 78 ~,~ n = ? $$ | 4 |
| 2046 | Find $ a_35 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2047 | Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2048 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 324 ~~ \text{and} ~~ r = \frac{ 1 }{ 6 } $. | 4 |
| 2049 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $. | 4 |
| 2050 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $. | 4 |
