数列{an}满足a1=2,a2=5,a(n+2)=3a(n+1)-2an.(1)求证:数列{a(n+1)-an}是等比数列

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数列{an}满足a1=2,a2=5,a(n+2)=3a(n+1)-2an.(1)求证:数列{a(n+1)-an}是等比数列数列{an}满足a1=2,a2=5,a(n+2)=3a(n+1)-2an.(1

数列{an}满足a1=2,a2=5,a(n+2)=3a(n+1)-2an.(1)求证:数列{a(n+1)-an}是等比数列
数列{an}满足a1=2,a2=5,a(n+2)=3a(n+1)-2an.(1)求证:数列{a(n+1)-an}是等比数列

数列{an}满足a1=2,a2=5,a(n+2)=3a(n+1)-2an.(1)求证:数列{a(n+1)-an}是等比数列
a(n+2)=3a(n+1)-2an
a(n+2)-a(n+1))=2a(n+1)-2an a(n+2)-a(n+1))=2【a(n+1)-an 】
所以是等比数列

a(n+2)-a(n+1)=2a(n+1)-2an
a(n+1)-an =2an -2a(n-1)
……
a3 - a2 =2a2 -2a1
全部相乘
a(n+2)-a(n+1) = 2^n(a2-a1)=3*2^n
数列{a(n+1)-an}=2^(n-1)*3
得证

a(n+2)=a(n+1)+2a(n+1)-2an
a(n+2)-a(n+1)=2a(n+1)-2an
[a(n+2-a(n+1))]/[a(n+1)-2an]=2
带入a1 a2 a3 a4 均成立
所以综上所述 此数列是等比数量

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