设数列{an}为等比数列,数列{bn}满足bn=na1+(n-1)a2+…+2an-1+an,n∈N*,已知b1=m,b2=3m/2,其中m≠0.(Ⅰ)求数列{an}的首项和公比;
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![设数列{an}为等比数列,数列{bn}满足bn=na1+(n-1)a2+…+2an-1+an,n∈N*,已知b1=m,b2=3m/2,其中m≠0.(Ⅰ)求数列{an}的首项和公比;](/uploads/image/z/10342966-22-6.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%BA%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E6%95%B0%E5%88%97%7Bbn%7D%E6%BB%A1%E8%B6%B3bn%3Dna1%2B%EF%BC%88n-1%EF%BC%89a2%2B%E2%80%A6%2B2an-1%2Ban%2Cn%E2%88%88N%2A%2C%E5%B7%B2%E7%9F%A5b1%3Dm%2Cb2%3D3m%2F2%2C%E5%85%B6%E4%B8%ADm%E2%89%A00%EF%BC%8E%EF%BC%88%E2%85%A0%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E9%A6%96%E9%A1%B9%E5%92%8C%E5%85%AC%E6%AF%94%EF%BC%9B)
设数列{an}为等比数列,数列{bn}满足bn=na1+(n-1)a2+…+2an-1+an,n∈N*,已知b1=m,b2=3m/2,其中m≠0.(Ⅰ)求数列{an}的首项和公比;
设数列{an}为等比数列,数列{bn}满足bn=na1+(n-1)a2+…+2an-1+an,n∈N*,已知b1=m,b2=3m/2
,其中m≠0.
(Ⅰ)求数列{an}的首项和公比;
设数列{an}为等比数列,数列{bn}满足bn=na1+(n-1)a2+…+2an-1+an,n∈N*,已知b1=m,b2=3m/2,其中m≠0.(Ⅰ)求数列{an}的首项和公比;
解,因为{bn}满足bn=na1+(n-1)a2+…+2an-1+an,n∈N*,所以,令n=1,得,b1=a1,所以首相 a1=m.
令n=2,得,b2=2 a1+a2.因为b2=3m/2,a1=m.所以 3m/2=2 m+a2.得a2=-m/2;
所以,公比q=a2/a1=-1/2.
b1=a1=m
b2=2a1+a2=3m/2
a2=-m/2
q=a2/a1=-1/2
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