已知数列{an}中满足(An+1-An)(An+1+An)=16,且a1=1,an

已知数列{an}中满足(An+1-An)(An+1+An)=16,且a1=1,an
已知数列{an}中满足(An+1-An)(An+1+An)=16,且a1=1,an

已知数列{an}中满足(An+1-An)(An+1+An)=16,且a1=1,an
1.
[a(n+1)-an][a(n+1)+an]=16
a(n+1)²-an²=16,为定值.
a1=1 a1²=1
数列{an²}是以1为首项,16为公差的等差数列.
2.
an²=1+16(n-1)=16n-15
n≥2时,16n-15≥16×2-15=17>0
an