Geometric sequences

Find $ a_20 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 2 $.

Find $ a_16 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 2 $.

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

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 9 }{ 5 } $.

Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.

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

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

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = 1.66 $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 16 } ~~ \text{and} ~~ r = \frac{ 27 }{ 64 } $.

Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -4 $.

Find $ a_14 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = -3 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.

Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.005 $.

Find the sum of the first $ 36 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = 1.005 $.

Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -4 $.

Find $ a_2 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 100 } ~~ \text{and} ~~ r = -10 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 625 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.

Find first element ( $ a_1 $ ) of a geometic progression if $ r = -2 ~~ \text{and} ~~ a_{ 8 } = 124 $.

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

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.

Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.

Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 40000 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.

Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 10 $.

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

Find $ a_14 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.

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

Find $ a_12 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.

Find $ a_15 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.

Find $ a_21 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $.

Find $ a_25 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $.

Find $ a_23 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $.

Find $ a_144 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $.

Find $ a_100 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $.

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

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 17 }{ 250 } ~~ \text{and} ~~ r = \frac{ 17 }{ 25 } $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 59049 ~~ \text{and} ~~ r = \frac{ 5 }{ 3 } $.

Find $ a_70 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $.

Find $ a_64 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $.

Find $ a_57 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 1.5 $.

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

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

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 5 } ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $.

Find $ a_5 $ of a geometric progression if $ a_1 = 512 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find $ a_11 $ of a geometric progression if $ a_1 = 3246 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.

Find $ a_21 $ of a geometric progression if $ a_1 = 4000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.