正项等比数列an的前n项积为Tn,且T5^6/T3^5=32,则a4=

题目

正项等比数列an的前n项积为Tn,且T5^6/T3^5=32,则a4=

答案

正项等比数列an的前n项积为Tn
T5=a1a2a3a4a5=a3^5
T3=a1a2a3=a2^3
T5^6/T3^5
=a3^30/a2^15
=a3^15*(a3/a2)^15
=a3^15*q^15
=(a3q)^15=32
a4^15=2^5
a4^3=2
a4=三次根号下2