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 = 1 B1 = -1求{An}、｛Bn｝通项公式
问题描述：
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
答
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=2C1=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...