Geometric sequences

Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.

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

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

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -4 $.

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

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

Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 1 $.

Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.

Find $ a_2 $ of a geometric progression if $ a_1 = 98 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 7 } $.

Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $.

Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 128 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -11 ~~ \text{and} ~~ r = -4 $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.

Find $ a_10 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $.

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

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

Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.

Find the sum of the first $ 9223372036854775807 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

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

Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $.

Find $ a_6 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

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

Find $ a_2 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 4 $.

Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = -78125 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $.

Find $ a_50 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -10 $.

Find $ a_36 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 12 $.

Find $ a_294 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = -42 $.

Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 8 } $.

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

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -2 $.