已知数例{An}满足a1=1,a2=2,A(n+2)=2An+A(n+1)
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已知数例{An}满足a1=1,a2=2,A(n+2)=2An+A(n+1)
(1)求a3,a4,a5 (2)猜想这个数例的通项公式,并验证此通项公式是否满足递推公式.
(1)求a3,a4,a5 (2)猜想这个数例的通项公式,并验证此通项公式是否满足递推公式.
![已知数例{An}满足a1=1,a2=2,A(n+2)=2An+A(n+1)](/uploads/image/z/20140676-44-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E4%BE%8B%7BAn%7D%E6%BB%A1%E8%B6%B3a1%3D1%2Ca2%3D2%2CA%28n%2B2%29%3D2An%2BA%28n%2B1%29)
1,a3=2a1+a2=4;
a4=2a2+a3=8;
a5=2a3+a4=16,
2,猜测 an=2^(n-1),
验证:A(n+2)=2^(n+1),A(n+1)=2^n,2An=2^n,
那么A(n+2)=2An+A(n+1).
a4=2a2+a3=8;
a5=2a3+a4=16,
2,猜测 an=2^(n-1),
验证:A(n+2)=2^(n+1),A(n+1)=2^n,2An=2^n,
那么A(n+2)=2An+A(n+1).
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