已知等比数列(an)中,a1+a2=9,a1a2a3=27,sn=?我还是求不出a1和q,怎么求

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已知等比数列(an)中,a1+a2=9,a1a2a3=27,sn=?我还是求不出a1和q,怎么求
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已知等比数列(an)中,a1+a2=9,a1a2a3=27,sn=?我还是求不出a1和q,怎么求
已知等比数列(an)中,a1+a2=9,a1a2a3=27,sn=?
我还是求不出a1和q,怎么求

已知等比数列(an)中,a1+a2=9,a1a2a3=27,sn=?我还是求不出a1和q,怎么求
设公比为q.
a1+a2=a1(1+q)=9
a1a2a3=a1^3q^^3=27
a1q=3
a1=3/q
(3/q)(1+q)=9
3q+3=9q
6q=3
q=1/2
a1=3/(1/2)=6
Sn=a1(1-q^n)/(1-q)
=6*[1-(1/2)^n]/(1-1/2)
=12[1-(1/2)^n]
=12(2^n-1)/2^n

设公比是q,那么有:
a1+a2=a1(1+q)=9
a1a2a3=a1^3*q^3=27
=>((1+q)/q)^3=9^3/27=3^3
=>(1+q)/q=3
=>q=1/2
=>a=9/(1+q)=9/(3/2)=6
=》Sn=a(1-q^n)/(1-q)=12*(1-(1/2)^n)