Question

数列｛an}中,a1=1,2的a（n+1）次方-2的an次方=3,求通向公式

Answer 1

2^[a(n+1)]-2^[a(n)]=3,

2^[a(n)]-2^[a(n-1)]=3,

...

2^[a(2)]-2^[a(1)]=3,

上面n个等式相加,有

2^[a(n+1)]-2^[a(1)]=3n,

2^[a(n+1)]=3n+2,

a(n+1)=log_{2}[3n+2],

又,a(1)=1,

所以,通项公式为,

a(n)=log_{2}[3n-1],n=1,2,...