In a geometric sequence, the fourth term is -4, and the eighth term is -324. What is the tenth term?

Answer 1

t(4) = ar^3 = -4
t(8) = ar^7 = -324
divide t(8) by t(4)
r^4 = 81
r = 81^(1/4) = ± 3

if r = +3
in t(4)
a(3^3) = -4
a = -4/27
t(10) = (-4/27)(3^9) = -2916

if r = -3
a = -4/-27 = 4/27
t(10) = ar^9 = (4/27)(-3)^9 = 4(-729) = -2916

either way, t(10) = -2916