Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
1851	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -3 $.	4
1852	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	4
1853	Find $ a_3 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 61 }{ 50 } $.	4
1854	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	4
1855	Find $ a_25 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	4
1856	Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	4
1857	$$ a_1 = 900 ~,~ r = \frac{ 1 }{ 50 } ~,~ a_n = 350 ~,~ n = ? $$	4
1858	Find $ a_20 $ of a geometric progression if $ a_1 = 30000 ~~ \text{and} ~~ r = 1.1 $.	4
1859	Find $ a_30 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = 1.1 $.	4
1860	Find $ a_20 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 1.1 $.	4
1861	Find $ a_30 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.1 $.	4
1862	Find $ a_15 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 1.1 $.	4
1863	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.	4
1864	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	4
1865	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	4
1866	Find $ a_26 $ of a geometric progression if $ a_1 = 82000 ~~ \text{and} ~~ r = 0.016 $.	4
1867	Find the sum of the first $ 360 $ terms of a geometric sequence if $ a_1 = 1100 ~~ \text{and} ~~ r = 1.05 $.	4
1868	Find $ a_19 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $.	4
1869	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 8 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4
1870	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	4
1871	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	4
1872	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	4
1873	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 12 } = \frac{ 15 }{ 8 } ~~ \text{and} ~~ a_{ 6 } = 120 $.	4
1874	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 8 $.	4
1875	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = \frac{ 32 }{ 3 } ~~ \text{and} ~~ a_{ 9 } = \frac{ 512 }{ 243 } $.	4
1876	Find $ a_12 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4
1877	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	4
1878	Find $ a_4 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4
1879	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	4
1880	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -192 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	4
1881	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 4 $.	4
1882	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 6 $.	4
1883	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 56 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	4
1884	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 5 } = 32 ~~ \text{and} ~~ a_{ 2 } = 4 $.	4
1885	Find $ a_9 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	4
1886	Find $ a_7 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	4
1887	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	4
1888	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	4
1889	Find $ a_4 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 2 $.	4
1890	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	4
1891	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 75 ~~ \text{and} ~~ r = 1.22 $.	4
1892	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $.	4
1893	Find $ a_61 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 0.98 $.	4
1894	Find the sum of the first $ 61 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 0.95 $.	4
1895	Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	4
1896	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 6 $.	4
1897	Find $ a_20 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	4
1898	Find $ a_16 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	4
1899	Find $ a_18 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	4
1900	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	4