急!高一数学:1.数列{an}中,Sn是其前n项和,若a1=1,a(n+1)=1⼀3Sn(n≥1)则an=?

2025-01-01 22:31:23
推荐回答(1个)
回答1:

  1. 因为an=sn-s(n-1)=3a(n+1)-3an
      所以a(n+1)=4/3 an

    {1,4/3,16/9,......}

    an=(4/3)的n-1次幂

  2. n=1 ,a1=1/4(a1+1)²,得到a1=1

    s(n-1)=sn-an

    1/4[a(n-1)+1]²=1/4(an+1)²-an

    [a(n-1)+1]²=(an+1)²-4an=(an-1)²

    a(n-1)+1=an-1

    an=a(n-1)+2

    {1,3,5,.....}

    an=2n-1

  3. an=根号下(an)²+1   题目错误