Geometric sequences

(the database of solved problems)

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

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ID	Problem	Count
7901	Find $ a_17 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	1
7902	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	1
7903	Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	1
7904	Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 1 $.	1
7905	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = 2 $.	1
7906	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
7907	Find $ a_8 $ of a geometric progression if $ a_1 = 98000 ~~ \text{and} ~~ r = 1.025 $.	1
7908	Find the sum of the first $ 365 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
7909	Find the sum of the first $ 332 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	1
7910	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -6 $.	1
7911	Find $ a_14 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	1
7912	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	1
7913	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 7 }{ 5 } $.	1
7914	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 7 ~~ \text{and} ~~ a_{ 4 } = 56 $.	1
7915	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 8 }{ 11 } $.	1
7916	Find $ a_20 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	1
7917	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -\frac{ 3 }{ 2 } $.	1
7918	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = -0.1667 $.	1
7919	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 1 }{ 2 } ~~ \text{and} ~~ a_{ 3 } = 64 $.	1
7920	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
7921	Find $ a_5 $ of a geometric progression if $ a_1 = 0.0175 ~~ \text{and} ~~ r = -5 $.	1
7922	Find $ a_5 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
7923	Find $ a_10 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
7924	Find $ a_10 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
7925	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 99 }{ 100 } $.	1
7926	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
7927	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 46 }{ 99 } $.	1
7928	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 21 }{ 20 } $.	1
7929	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.	1
7930	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	1
7931	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	1
7932	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 27 }{ 10 } ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	1
7933	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2.7 ~~ \text{and} ~~ r = 0.1 $.	1
7934	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = 0.1 $.	1
7935	Find $ a_10 $ of a geometric progression if $ a_1 = 2.7 ~~ \text{and} ~~ r = 0.1 $.	1
7936	Find $ a_10 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 0.8 $.	1
7937	Find $ a_208 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 1 $.	1
7938	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
7939	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 0.1 ~~ \text{and} ~~ r = 2 $.	1
7940	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 81 } ~~ \text{and} ~~ r = 3 $.	1
7941	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 6851 }{ 100 } ~~ \text{and} ~~ r = 1.184 $.	1
7942	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 24 ~~ \text{and} ~~ r = -2 $.	1
7943	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
7944	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7500 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	1
7945	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	1
7946	Find $ a_10 $ of a geometric progression if $ a_1 = 162.2 ~~ \text{and} ~~ r = 1.01 $.	1
7947	Find $ a_72 $ of a geometric progression if $ a_1 = 162.2 ~~ \text{and} ~~ r = 1.01 $.	1
7948	Find $ a_6 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
7949	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 39000 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.	1
7950	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	1