Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 1801 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $. | 4 |
| 1802 | Find $ a_9 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 6 $. | 4 |
| 1803 | Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.15 $. | 4 |
| 1804 | Find $ a_12 $ of a geometric progression if $ a_1 = 12000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 4 |
| 1805 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 15624 ~~ \text{and} ~~ r = 5 $. | 4 |
| 1806 | Find the sum of the first $ 48 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $. | 4 |
| 1807 | Find $ a_18 $ of a geometric progression if $ a_1 = 900 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 4 |
| 1808 | Find first element ( $ a_1 $ ) of a geometic progression if $ r = -\frac{ 1 }{ 3 } ~~ \text{and} ~~ a_{ 5 } = -6 $. | 4 |
| 1809 | Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $. | 4 |
| 1810 | Find $ a_15 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $. | 4 |
| 1811 | Find the sum of the first $ 56 $ terms of a geometric sequence if $ a_1 = 500 ~~ \text{and} ~~ r = 1.039 $. | 4 |
| 1812 | Find $ a_1 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 4 |
| 1813 | $$ a_1 = 1 ~~,~~ r = -2 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 4 |
| 1814 | Find $ a_3 $ of a geometric progression if $ a_1 = 171 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 4 |
| 1815 | $$ a_1 = -4 ~~,~~ r = -3 ~~,~~ a_1 = ? ~~,~~ r = ? $$ | 4 |
| 1816 | Find $ a_25 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $. | 4 |
| 1817 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $. | 4 |
| 1818 | Find $ a_5 $ of a geometric progression if $ a_1 = 0.002 ~~ \text{and} ~~ r = 6 $. | 4 |
| 1819 | Find $ a_6 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $. | 4 |
| 1820 | Find $ a_2 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 4 |
| 1821 | Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 4 |
| 1822 | Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 5 } $. | 4 |
| 1823 | Find $ a_10 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $. | 4 |
| 1824 | Find $ a_10 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $. | 4 |
| 1825 | Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 25 } ~~ \text{and} ~~ r = 2 $. | 4 |
| 1826 | Find $ a_20 $ of a geometric progression if $ a_1 = 1692 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 4 |
| 1827 | Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $. | 4 |
| 1828 | Find $ a_7 $ of a geometric progression if $ a_1 = -15 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $. | 4 |
| 1829 | Find $ a_2 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $. | 4 |
| 1830 | Find $ a_6 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -4 $. | 4 |
| 1831 | Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $. | 4 |
| 1832 | $$ a_1 = 30 ~,~ r = \frac{ 1 }{ 3 } ~,~ S_n = 40 ~,~ n = ? $$ | 4 |
| 1833 | Find $ a_4 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 2 $. | 4 |
| 1834 | Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $. | 4 |
| 1835 | $$ a_1 = 6 ~,~ r = 2 ~,~ a_n = 1536 ~,~ n = ? $$ | 4 |
| 1836 | Find $ a_5 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 4 |
| 1837 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 3645 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $. | 4 |
| 1838 | Find $ a_8 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 4 |
| 1839 | Find $ a_6 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 4 |
| 1840 | Find $ a_6 $ of a geometric progression if $ a_1 = 7640 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $. | 4 |
| 1841 | Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $. | 4 |
| 1842 | Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $. | 4 |
| 1843 | Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 59 }{ 5 } $. | 4 |
| 1844 | Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 5 } $. | 4 |
| 1845 | Find $ a_2 $ of a geometric progression if $ a_1 = 11000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 100 } $. | 4 |
| 1846 | Find $ a_70 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 0.2 $. | 4 |
| 1847 | Find $ a_70 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 1.2 $. | 4 |
| 1848 | Find the sum of the first $ 70 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 1.02 $. | 4 |
| 1849 | Find $ a_10 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 2 $. | 4 |
| 1850 | Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $. | 4 |
