尽量详细点)已知数列{An}、｛Bn｝A n+1 = 8 An - 6 Bn B n+1 = 6 An - 4 BnA1

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/04/28 06:56:54

尽量详细点)
已知数列{An}、｛Bn｝
A n+1 = 8 An - 6 Bn
B n+1 = 6 An - 4 Bn
A1 = 1
B1 = -1
求{An}、｛Bn｝通项公式

A n+1-B n+1=8 An - 6 Bn -(6 An - 4 Bn )=2(An - Bn)
所以设Cn=An - Bn
那么Cn+1=A n+1-B n+1
所以Cn+1/Cn=2
所以Cn是等差数列,q=2
C1=A1-B1=2
所以Cn=An - Bn=2^n
代如A n+1 = 8 An - 6 Bn
所以 A n+1=8 An - 6 Bn =2An+6*2^n
所以
A n+1 =2An+6*2^n
2A n=2^2An-1+6*2^n-1
2^2An-1=2^3An-2+6*2^n-2
………………
………………
2^n-1A2=2^nA1+6*2^1
然后左右想加得
A n+1=2^nA1+6*(2+4+8+16+……+2^n)
因为A1=1
所以A n+1=2^n+6*(2^n+1 -2)
所以A n=2^n-1+6*2^n-12
而Bn=2^n-1+5*2^n-12
A n等于2的n-1次方+6*2的n次方-12

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