Geometric sequences

Find $ a_6 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.

Find $ a_4 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 5 $.

Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.

Find $ a_3 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.

Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.

Find $ a_11 $ of a geometric progression if $ a_1 = 3.9 ~~ \text{and} ~~ r = 6.923 $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 224 ~~ \text{and} ~~ r = 2 $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 8 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

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

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

Find $ a_6 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 6 $.

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

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

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $.

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

Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 5 } $.

Find $ a_7 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.

Find $ a_6 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 3 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.

Find $ a_4 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 5 $.

Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 6 $.

Find $ a_13 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.

Find $ a_34 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -2 $.

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

Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.

Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 0.22 $.

Find $ a_15 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $.

Find $ a_15 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.

Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $.

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

Find $ a_5 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 18 $.

Find $ a_5 $ of a geometric progression if $ a_1 = 125 ~~ \text{and} ~~ r = -5 $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 2 $.

Find $ a_13 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = 2 $.

Find $ a_14 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = 2 $.

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

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.

Find $ a_5 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $.

Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 1 }{ 2 } $.

Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 4 $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 150000 ~~ \text{and} ~~ r = 0.5 $.

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

Find $ a_8 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.

Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 64 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -8 $.

Find $ a_11 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $.