The fifth term of a geometric sequence of positive numbers is $11$ and the eleventh term is $5$. What is the eighth term of the sequence? Express your answer in simplest radical form.
Let a1 be the first term
So....we have that
11 / 5 = a1 (r)^4 / [ a1 (r)^10]
11/5 = r^4/r^10
11/5 = 1/ r^6
r^6 = (5/11)
r = (5/11)^(1/6)
So...the eighth term is
11 * [(5/11)^(1/6)]^3 =
11 ( 5/11)^(1/2) =
11 √5/ √11 =
√11*√5 =
√55
