已知{an}中,a1=1,a2,3an+2-5a(n+1)下标+2an=0,令bn=a(n+1)下标-an,求证{bn}成等比数列

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已知{an}中,a1=1,a2,3an+2-5a(n+1)下标+2an=0,令bn=a(n+1)下标-an,求证{bn}成等比数列

已知{an}中,a1=1,a2,3an+2-5a(n+1)下标+2an=0,令bn=a(n+1)下标-an,求证{bn}成等比数列
已知{an}中,a1=1,a2,3an+2-5a(n+1)下标+2an=0,令bn=a(n+1)下标-an,求证{bn}成等比数列

已知{an}中,a1=1,a2,3an+2-5a(n+1)下标+2an=0,令bn=a(n+1)下标-an,求证{bn}成等比数列
3a[n+2]-5a[n+1]+2a[n]=0
所以
3(a[n+2]-a[n+1])=2(a[n+1]-a[n])
b[n]=a[n+1]-a[n]
所以
3b[n+1]=2b[n]
b[n+1]=2/3b[n]
b[1]=a[2]-a[1]不等于0
所以b[n]成等比数列