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
1901	Find $ a_8 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 8 } ~~ \text{and} ~~ r = 2 $.	4
1902	Find $ a_8 $ of a geometric progression if $ a_1 = 112 ~~ \text{and} ~~ r = -4 $.	4
1903	Find $ a_4 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = \dfrac{ 77 }{ 25 } $.	4
1904	Find $ a_3 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = \dfrac{ 77 }{ 25 } $.	4
1905	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 25 ~~ \text{and} ~~ a_{ 2 } = 77 $.	4
1906	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 25 ~~ \text{and} ~~ a_{ 4 } = 680 $.	4
1907	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 25 ~~ \text{and} ~~ a_{ 3 } = 226 $.	4
1908	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 25 ~~ \text{and} ~~ a_{ 4 } = 680 $.	4
1909	$$ a_1 = 226 ~,~ r = \frac{ 301 }{ 100 } ~,~ a_n = 4 ~,~ n = ? $$	4
1910	Find $ a_3 $ of a geometric progression if $ a_1 = 226 ~~ \text{and} ~~ r = 3.01 $.	4
1911	Find $ a_2 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 3.08 $.	4
1912	Find $ a_7 $ of a geometric progression if $ a_1 = 25 ~~ \text{and} ~~ r = 3.08 $.	4
1913	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 1 ~~ \text{and} ~~ a_{ 40 } = 70 $.	4
1914	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.11 $.	4
1915	Find $ a_40 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.11 $.	4
1916	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.115 $.	4
1917	Find $ a_5 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = \dfrac{ 17 }{ 20 } $.	4
1918	Find $ a_5 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	4
1919	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	4
1920	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	4
1921	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	4
1922	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	4
1923	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	4
1924	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 800 ~~ \text{and} ~~ r = 0.98 $.	4
1925	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 352 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	4
1926	Find $ a_4 $ of a geometric progression if $ a_1 = -768 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 64 } $.	4
1927	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1280 }{ 567 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	4
1928	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 23 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 65 } $.	4
1929	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $.	4
1930	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $.	4
1931	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $.	4
1932	Find $ a_4 $ of a geometric progression if $ a_1 = 16384 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	4
1933	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $.	4
1934	Find $ a_8 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 1.05 $.	4
1935	Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	4
1936	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $.	4
1937	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 20 } ~~ \text{and} ~~ r = 2 $.	4
1938	Find $ a_7 $ of a geometric progression if $ a_1 = -\dfrac{ 4 }{ 5 } ~~ \text{and} ~~ r = -5 $.	4
1939	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -9 ~~ \text{and} ~~ r = 8 $.	4
1940	Find $ a_7 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	4
1941	Find $ a_13 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	4
1942	Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	4
1943	Find $ a_13 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.	4
1944	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 30000 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $.	4
1945	Find $ a_20 $ of a geometric progression if $ a_1 = 121 ~~ \text{and} ~~ r = 0.016 $.	4
1946	Find $ a_9 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 4 $.	4
1947	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 4 $.	4
1948	Find $ a_6 $ of a geometric progression if $ a_1 = 24 ~~ \text{and} ~~ r = 8 $.	4
1949	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	4
1950	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	4