Geometric sequences

Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.

Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.41 $.

Find $ a_28 $ of a geometric progression if $ a_1 = 90 ~~ \text{and} ~~ r = 0.971 $.

Find the sum of the first $ 28 $ terms of a geometric sequence if $ a_1 = 90 ~~ \text{and} ~~ r = 0.971 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.

Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 256 } ~~ \text{and} ~~ r = -4 $.

Find $ a_12 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find $ a_2 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.

Find $ a_3 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.

Find $ a_4 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.

Find $ a_9 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.

Find $ a_11 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.

Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -5 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = 1.1 $.

Find the sum of the first $ 24 $ terms of a geometric sequence if $ a_1 = 14 ~~ \text{and} ~~ r = 1.1 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2700 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.

Find $ a_7 $ of a geometric progression if $ a_1 = 2700 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.

Find $ a_30 $ of a geometric progression if $ a_1 = 16.21 ~~ \text{and} ~~ r = 0.9345 $.

Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = \frac{ 87 }{ 25 } ~~ \text{and} ~~ r = 0.9433 $.

Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 4 ~~ \text{and} ~~ a_{ 3 } = 16 $.

Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 0.2 ~~ \text{and} ~~ r = 0.8 $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.

Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = -256 $.

Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = 2 $.

Find $ a_6 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = 2 $.

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = 2 $.

Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 0.09877 ~~ \text{and} ~~ r = 0.1975 $.

Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 6 ~~ \text{and} ~~ a_{ 4 } = 24 $.

Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 3 ~~ \text{and} ~~ a_{ 6 } = 24 $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.

Find $ a_12 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 6 $.

Find $ a_12 $ of a geometric progression if $ a_1 = 20000000 ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 3 } $.

Find $ a_12 $ of a geometric progression if $ a_1 = 20000000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.

Find $ a_12 $ of a geometric progression if $ a_1 = 20000000 ~~ \text{and} ~~ r = 0.3333 $.

Find $ a_12 $ of a geometric progression if $ a_1 = 20000000 ~~ \text{and} ~~ r = 0.75 $.

Find $ a_12 $ of a geometric progression if $ a_1 = 2000000 ~~ \text{and} ~~ r = 0.75 $.

Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.

Find $ a_2 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.

Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 77800 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 77800 ~~ \text{and} ~~ r = 1.25 $.

Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 77800 ~~ \text{and} ~~ r = 1.25 $.

Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.22 $.

Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 9 $.