已知f(x)=loga(x)(a>0且a≠1),且2,f(a1),f(a2),f(a3),...f(an),2n+4,...(n属于N*)成等差数列.（1）求数列{an}的通项公式?

题目

已知f(x)=loga(x)(a>0且a≠1),且2,f(a1),f(a2),f(a3),...f(an),2n+4,...(n属于N*)成等差数列.（1）求数列{an}的通项公式?

答案

分n为奇数和偶数讨论n为奇数时2+2n+4=2f(a(1/2n+1/2))n+3=loga a(1/2n+1/2)a(1/2n+1/2)=a^(n+3)an=a^(2n+2) n为奇数n为偶数时2+2n+4=f(a(n/2))+f(a(n/2+1))2n+6=loga a(n/2)+loga a(n/2+1)a^(2a+6)=a(n/2)+a(n/2+1)a...