Math
posted by Ally .
In a geometric sequence, the fourth term is 4, and the eighth term is 324. What is the tenth term?

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