Geometric sequences

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

Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

Find $ a_3 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -18 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 2 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = 5 $.

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

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

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 4 $.

Find $ a_25 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 8 $.

Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -3 $.

Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -4 $.

Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.

Find $ a_11 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 81 } ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.

Find $ a_11 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 81 } ~~ \text{and} ~~ r = -3 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -5 $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = 2 $.

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

Find $ a_2 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 1 $.

Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -2 $.

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.

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 $ 4 $ 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 = \frac{ 32 }{ 81 } ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 32 }{ 81 } ~~ \text{and} ~~ r = -\frac{ 3 }{ 2 } $.

Find $ a_15 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2.915 $.

Find $ a_2 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.

Find $ a_9 $ of a geometric progression if $ a_1 = 384 ~~ \text{and} ~~ r = 2 $.

Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = \dfrac{ 21 }{ 20 } $.

Find $ a_10 $ of a geometric progression if $ a_1 = 3125 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.

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

Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 8 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 7 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = 3 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 76 ~~ \text{and} ~~ r = 3 $.

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

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

Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 512 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

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

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

Find $ a_6 $ of a geometric progression if $ a_1 = -192 ~~ \text{and} ~~ r = -4 $.

Find $ a_13 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.

Find $ a_7 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -2 $.

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