Geometric sequences

Find $ a_3 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 3 $.

Find $ a_2 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 60 $.

Find $ a_45 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = 2 $.

Find $ a_4 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 7 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 2916 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = -2 $.

Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.

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

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = -3 $.

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

Find $ a_6 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = 37 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 10 } $.

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

Find $ a_1 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = 50 $.

Find $ a_2 $ of a geometric progression if $ a_1 = 150 ~~ \text{and} ~~ r = 50 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.

Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 0.5429 $.

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

Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 9 }{ 8 } ~~ \text{and} ~~ a_{ 3 } = \frac{ 1 }{ 2 } $.

Find $ a_6 $ of a geometric progression if $ a_1 = 500 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.

Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.

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

Find $ a_300 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.02 $.

Find $ a_600 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.02 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.23 $.

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

Find $ a_5 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -5 $.

Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.

Find $ a_157 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $.

Find $ a_12 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $.

Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = -\frac{ 5 }{ 2 } ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.

Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 2.9 ~~ \text{and} ~~ r = 0.87 $.

Find $ a_14 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.

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

Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 4 }{ 9 } $.

Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 32 }{ 81 } ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.

Find $ a_3 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 15 }{ 2 } $.

Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.

Find $ a_2 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 100 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = -2 $.

Find $ a_39 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.108 $.

Find $ a_39 $ of a geometric progression if $ a_1 = 1.7 ~~ \text{and} ~~ r = 1.112 $.

Find $ a_39 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.115 $.

Find the sum of the first $ 39 $ terms of a geometric sequence if $ a_1 = 1.7 ~~ \text{and} ~~ r = 1.115 $.

Find $ a_39 $ of a geometric progression if $ a_1 = \dfrac{ 3399 }{ 100 } ~~ \text{and} ~~ r = 1.116 $.

Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = 3 $.