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Un = ar^(n - 1)

a) 9, 27, 81, 243, ... => a = 9, r = 27/9 = 3
Un = ar^(n - 1) = 9 . 3^(n - 1) = 3^2 . 3^(n - 1) = 3^(2 + n - 1) = 3^(n + 1)
U9 = 3^(9 + 1) = 3^10 = 59.049

b) 8, 16, 32, 64, ... => a = 8, r = 16/8 = 2
Un = ar^(n - 1) = 8 . 2^(n - 1) = 2^3 . 2^(n - 1) = 2^(3 + n - 1) = 2^(n + 2)
U9 = 2^(9 + 2) = 2^11 = 2.048

c) 5, 15, 45, 135, ... => a = 5, r = 15/5 = 3
Un = ar^(n - 1) = 5 . 3^(n - 1)
U9 = 5 . 3^(9 - 1) = 5 . 3^8 = 5 (6.561) = 32.805

d) 7, 28, 112, 448, ... => a = 7, r = 28/7 = 4
Un = ar^(n - 1) = 7 . 4^(n - 1)
U9 = 7 . 4^(9 - 1) = 7 . 4^8 = 7 . (65.536) = 458.752

e) -2, 6, -18, 54, ....=> a = -2, r = 6/(-2) = -3
Un = ar^(n - 1) = -2 . (-3)^(n - 1)
U9 = -2 . (-3)^(9 - 1) = -2 . (-3)^8 = -2 (6.561) = -13.122

f) -1, -6, -36, -216, ... => a = -1, r = (-6)/(-1) = 6
Un = -1 . 6^(n - 1)
U9 = -1 . 6^(9 - 1) = -1 . 6^8 = -1.679.616

g) -3, 15, -75, 375, ... => a = -3, r = 15/(-3) = -5
Un = -3 . (-5)^(n - 1)
U9 = -3 . (-5)^8 = -3 . (390.625) = -1.171.875

h) 108, 36, 12, 4, ... => a = 108, r = 36/108 = 1/3
Un = 108 . (1/3)^(n - 1)
U9 = 108 . (1/3)^8 = 108 . 1/(6.561) = 4/243

i) 7, 14, 28, 56, ... => a = 7, r = 14/7 = 2
Un = 7 . 2^(n - 1)
U9 = 7 . 2^8 = 7 . 256 = 1.792

j) 4, -12, 36, -108, ... => a = 4, r = -12/4 = -3
Un = 4 . (-3)^(n - 1)
U9 = 4 . (-3)^8 = 4 . (6.561) = 26.244

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