等比数列an中,S2=7 S6=91,则S4=s2=a1(1-q^2)/(1-q)=7 ① s6=a1(1-q^6)/(1-q)=_数学解答

等比数列an中,S2=7 S6=91,则S4=
s2=a1(1-q^2)/(1-q)=7 ①
s6=a1(1-q^6)/(1-q)=91 ②
②/①,得q^4+q^2-12=0,q^2=3代入①得,(2)
a1/(1-q)=7/(1-3)=-7/2
s4=a1(1-q4)/(1-q)=(-7/2)*(1-3^2)=28
(2)中为什么②/①=q^4+q^2-12=0

人气：249 ℃　时间：2020-07-07 02:14:12

解答

解由②/①得
[a1(1-q^2)/(1-q)]/[a1(1-q^6)/(1-q)]=7/91
即(1-q^2)/(1-q^6)=1/13
即(1-q^6)=13(1-q^2)
即(1-(q^2）^3)=13(1-q^2)
即（1-q^2)(1+q^2+q^4)=13(1-q^2)
即(1+q^2+q^4)=13
即q^4+q^2-12=0.