s2=3,s6=63,s4=等比数列{An},S2=3,S6=63.则S4等于?

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s2=3,s6=63,s4=等比数列{An},S2=3,S6=63.则S4等于?s2=3,s6=63,s4=等比数列{An},S2=3,S6=63.则S4等于?s2=3,s6=63,s4=等比数列{A

s2=3,s6=63,s4=等比数列{An},S2=3,S6=63.则S4等于?
s2=3,s6=63,s4=
等比数列{An},S2=3,S6=63.则S4等于?

s2=3,s6=63,s4=等比数列{An},S2=3,S6=63.则S4等于?
由于{An}是等比数列,设首项为a1,公比为q,
则由S2=3,可得 a1 + a1*q = 3 (1)
由 S6 =63,可知 a1 + a1*q + a1*q^2 + a1*q^3 + a1*q^4 + a1*q^5 = 63 (2)
把(1)式代入(2)式整理得 a1*q^2 + a1*q^3 + a1*q4 + a1*q^5 = 60
再对上式左边进行分组得:q^2(a1+ a1*q) + q^4(a1+a1*q) = 60 (3)
又把(1)式代入(3)式整理得 q^4 + q^2 - 20 = 0
q^2 = 4,q^2=-5 (舍去),所以 q=-2 或 q = 2
当q = -2时,由(1)可得 a1 = -3
此时 S4 =[a1(1-(-2)^4]/[1-(-2)] = 15
当q = 2时,由(1)可得 a1 = 1,
此时,S4 = [a1(1-2^4)]/(1-2) = 15
综上所述,S4=15