等比数列简单题

S2＝7 S6＝91
a1(1-q＾2)/(1-q)=7, (1)
a1(1-q＾6)/(1-q)=91
两式相除得(1-q＾6)/(1-q＾2)=13
【1-(q＾2)＾3】/(1-q＾2)=13
(1-q＾2)(1+q＾2+q＾4)/(1-q＾2)=13
q＾4+q＾2-12=0,q＾2=3
s4=a1(1-q＾4)/(1-q), (2)
(2)除以(1)
s4/s2=(1-q＾4)/(1-q＾2)
s4/7=4
s4=28

＾2表示平方

Sn=[A1(1-q^n)]/(1-q)
s2=a1(1-q^2)/1-q=a1(1+q)
a1(1+q)=7
s6=a1(1-q^6)/1-q
s6/s2=13
(1-q^6)/(1-q^2)=13
1-q^6=13(1-q^2)
1-q^6=13-13q^2
q^6-13q^2+12=0
q=1(舍),q=√3
s4=a1(1-q^4)/1-q
=s2*(1+q^2)
=7*(1+3)
=28

s2=a1+a2=a1+a1*q=a1*(1+q)=7
s6=a1+a2+a3+a4+a5+a6
=a1+a1*q+a1*q^2+a1*q^3+a1*q^4+a1*q^5
=s2+a1(q^2+q^3+q^4+q^5)
=7+a1(q^2+q^3+q^4+q^5)
=91
a1(q^2+q^3+q^4+q^5)=84
a1*q^2(1+q+q^2+q^3)=84
q^2*a1(1+q)+q^2*a1*q^2(1+q)=84
q^2*7+q^4*7=84
q^2+q^4=12
q^2(1+q^2)=3*4=12
q^2=3

s4=a1+a2+a3+A4
=s2+a3+a4
=7+a1*q^2+a1*q^3
=7+a1*q^2(1+q)
=7+3*7