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
5951	Find $ a_7 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = 4 $.	2
5952	Find $ a_7 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
5953	Find the sum of the first $ 99999999 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 0.97 $.	2
5954	Find the sum of the first $ 999999999999999999 $ terms of a geometric sequence if $ a_1 = 0.01 ~~ \text{and} ~~ r = 0.99 $.	2
5955	Find $ a_40 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	2
5956	Find $ a_7 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 10 $.	2
5957	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 7 }{ 10 } $.	2
5958	Find $ a_10 $ of a geometric progression if $ a_1 = 7300000000 ~~ \text{and} ~~ r = 1.012 $.	2
5959	Find $ a_13 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	2
5960	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 6 $.	2
5961	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 384 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	2
5962	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = 1 ~~ \text{and} ~~ a_{ 3 } = 9 $.	2
5963	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 25 ~~ \text{and} ~~ a_{ 6 } = \frac{ 25 }{ 64 } $.	2
5964	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = \frac{ 8 }{ 9 } ~~ \text{and} ~~ a_{ 7 } = \frac{ 64 }{ 243 } $.	2
5965	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 1 }{ 10 } ~~ \text{and} ~~ a_{ 2 } = 4 $.	2
5966	Find first element ( $ a_1 $ ) of a geometic progression if $ r = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ a_{ 3 } = 8 $.	2
5967	Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 8 $.	2
5968	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $.	2
5969	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 21 }{ 25 } $.	2
5970	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = \frac{ 41 }{ 4 } $.	2
5971	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = 4 $.	2
5972	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = 4 $.	2
5973	Find $ a_9 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5974	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5975	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
5976	Find $ a_6 $ of a geometric progression if $ a_1 = 130 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5977	Find $ a_6 $ of a geometric progression if $ a_1 = 135 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
5978	Find $ a_6 $ of a geometric progression if $ a_1 = -3200 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	2
5979	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $.	2
5980	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5981	Find $ a_2 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5982	Find $ a_5 $ of a geometric progression if $ a_1 = 347 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	2
5983	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 96 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5984	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 96 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5985	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 96 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
5986	Find $ a_8 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
5987	Find $ a_11 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
5988	Find $ a_11 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	2
5989	Find $ a_6 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	2
5990	Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 87 }{ 100 } $.	2
5991	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 2 }{ 9 } $.	2
5992	Find $ a_8 $ of a geometric progression if $ a_1 = 1000000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	2
5993	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	2
5994	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 0.075 $.	2
5995	Find $ a_5 $ of a geometric progression if $ a_1 = 0.00075 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $.	2
5996	Find $ a_4 $ of a geometric progression if $ a_1 = 0.02 ~~ \text{and} ~~ r = -3 $.	2
5997	Find $ a_10 $ of a geometric progression if $ a_1 = 0.02 ~~ \text{and} ~~ r = -3 $.	2
5998	Find $ a_112 $ of a geometric progression if $ a_1 = 0.02 ~~ \text{and} ~~ r = -3 $.	2
5999	Find the sum of the first $ 837 $ terms of a geometric sequence if $ a_1 = -80 ~~ \text{and} ~~ r = 5 $.	2
6000	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2