高一数学数列选择题
正项的等比数列{An}中,S2=7,S6=91,则S4=( )
A:28
B:32
C:35
D:49
参考答案:A.28
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,a1/(1-q)=7/(1-3)=-7/2
s4=a1(1-q4)/(1-q)=(-7/2)*(1-3^2)=28
正项的等比数列{An}中,S2=7,S6=91,则S4=( )
A:28
B:32
C:35
D:49
参考答案:A.28
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,a1/(1-q)=7/(1-3)=-7/2
s4=a1(1-q4)/(1-q)=(-7/2)*(1-3^2)=28