1.等比数列{an}中,a1=9,公比q

题目

1.等比数列{an}中,a1=9,公比q

答案

1.(a5)^2=a3a7=1/81
因为a1=9>0,q0
a5=1/9
2.s4=a1(1-q^4)/(1-q)=4
s8=a1(1-q^8)/(1-q)=16
s8/s4=(1-q^8)/(1-q^4)=4
q^8-4q^4+3=0
(q^4-1)(q^4-3)=0
q^4=3
又因a1(1-q^4)/(1-q)=4
a1/(1-q)=4/(1-q^4)=4/(1-3)=-2
s12=a1(1-q^12)/(1-q)=-2(1-q^12)=-2(1-3^3)=52