Geometric sequences

Find $ a_10 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 9 } $.

Find $ a_30 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.

Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 8 } = \frac{ 2 }{ 3 } ~~ \text{and} ~~ a_{ 5 } = 18 $.

Find $ a_25 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.

Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 729 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.

Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 729 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.

Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.

Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = -14 $.

Find $ a_4 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -5 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.

Find $ a_1 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find $ a_2 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find $ a_7 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 243 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.

Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.

Find $ a_8 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.

Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 8 } = 6250 ~~ \text{and} ~~ a_{ 4 } = 10 $.

Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 26 ~~ \text{and} ~~ r = 5 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 26 ~~ \text{and} ~~ r = 5 $.

Find $ a_9 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = -6 $.

Find $ a_13 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 2 $.

Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 125 }{ 8 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 125 }{ 8 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = 125 ~~ \text{and} ~~ a_{ 10 } = \frac{ 125 }{ 64 } $.

Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.

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

Find $ a_2 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.

Find $ a_4 $ of a geometric progression if $ a_1 = -54 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.

Find $ a_4 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 10 $.

Find $ a_3 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -5 $.

Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 16 } ~~ \text{and} ~~ r = 2 $.

Find $ a_4 $ of a geometric progression if $ a_1 = 2400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.

Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.

Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 64 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.

Find $ a_1 $ of a geometric progression if $ a_1 = 1875 ~~ \text{and} ~~ r = 0.2 $.

Find $ a_3 $ of a geometric progression if $ a_1 = 1875 ~~ \text{and} ~~ r = 0.2 $.

Find $ a_4 $ of a geometric progression if $ a_1 = 1451607 ~~ \text{and} ~~ r = 1.02 $.

Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 8 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 55000 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.

Find $ a_3 $ of a geometric progression if $ a_1 = 48 ~~ \text{and} ~~ r = 12 $.

Find $ a_7 $ of a geometric progression if $ a_1 = -17 ~~ \text{and} ~~ r = 3 $.

Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 1 }{ 2 } ~~ \text{and} ~~ a_{ 8 } = -\frac{ 5 }{ 8 } $.

Find $ a_12 $ of a geometric progression if $ a_1 = -80 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -48 ~~ \text{and} ~~ r = -2 $.