等比数列{an}中,a1a2a3a4a5=243,求a3

问题描述:

等比数列{an}中,a1a2a3a4a5=243,求a3

设公比为q
则a3=a1*q^2,所以a1=a3/q^2
则a2=a3/q
a4=a3*q
a5=a3*q^2
a1a2a3a4a5=a3/q^2*a3/q*a3*a3*q*a3*q^2=(a3)^5=243,
所以a3=3
解毕