求数列通项公式(高中数学)
an是正数数列,已知4Sn={[a(n+1)]^2}-4n-1,且a2,a5,a14构成等比数列,求数列an通项公式.
人气:206 ℃ 时间:2020-01-27 14:29:11
解答
1、
4S1=a²2-4*1-1
S1=a1
a²2=4a1+5
a2=√(4a1+5)
2、
an=Sn-S(n-1)
4an=4Sn-4S(n-1)
=a²(n+1)-4n-1-[a²n-4(n-1)-1]
=a²(n+1)-4-a²n
a²n+4an+4=a²(n+1)
(an+2)²=a²(n+1)
各项均匀为正数
an+2=a(n+1)
a1+2=a2=√(4a1+5)
a1²+4a1+4=4a1+5
a1=1
{an}是一个首项是1,公差是2的等差数列
an=2n-1
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