已知数列{an｝满足a1=1,a2=r(r>0),数列｛bn}是公比为q的等比数列（q>0),bn=ana(n+1),c

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已知数列{an｝满足a1=1,a2=r(r>0),数列｛bn}是公比为q的等比数列（q>0),bn=ana(n+1),cn=a(2n-1)+a2n,求cn

1 = a1a2 = r,故bn = r*q^(n-1)
又b(n+1)/bn = a(n+1)*a(n+2)/(an*a(n+1)) = a(n+2)/an、b(n+1)/bn = q
可得当n为奇数时an = a1*q^((n+1)/2 - 1) = q^((n-1)/2)
当n为偶数时an = a2*q^(n/2 - 1) = r*q^(n/2 - 1)
cn = a(2n-1)+a2n = q^(n-1) + r*q^(n-1) = (1+r)*q^(n-1)

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